Question 1

Let $f ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 x - \frac { 1 } { 5 }$ The set of all critical numbers of ƒ is

Accepted Answer

A)  $\{ - 1 \}$ 
B)  $\{ - 5 \}$ 
C)  $\{ - 1 , - 5 \}$ 
D)  $\{ 1,5 \}$ 
E)  $\varnothing$ 
A)  $\{ - 1 \}$ 
B)  $\{ - 5 \}$ 
C)  $\{ - 1 , - 5 \}$ 
D)  $\{ 1,5 \}$ 
E)  $\varnothing$ D

Question 2

Let $A = ( 10 + x ) ^ { 2 }$ If $\frac { d x } { d t } = \frac { 2 } { 15 }$ when then $\frac { d A } { d t }$ is

Accepted Answer

A) 8 
B) 6 
C) 4 
D) 2 
E)  $\frac { 1 } { 2 }$ 
A) 8 
B) 6 
C) 4 
D) 2 
E)  $\frac { 1 } { 2 }$ C

Question 3

The antiderivative of $f ( x ) = 6 - 3 x ^ { - 4 }$ is

Accepted Answer

A)  $12 x ^ { - 5 } + C$ 
B)  $6 x + x ^ { - 3 } + C$ 
C)  $6 x - x ^ { - 3 } + C$ 
D)  $6 x - \frac { x ^ { - 3 } } { 3 } + C$ 
E)  $- 6 x + x ^ { - 3 } + C$ 
A)  $12 x ^ { - 5 } + C$ 
B)  $6 x + x ^ { - 3 } + C$ 
C)  $6 x - x ^ { - 3 } + C$ 
D)  $6 x - \frac { x ^ { - 3 } } { 3 } + C$ 
E)  $- 6 x + x ^ { - 3 } + C$ B

Question 4

An isosceles triangle has equal sides 4 cm long and the included angle ?. If $\frac { d \theta } { d t } = 2 \mathrm { rad } / \mathrm { min }$ when $\theta = \frac { \pi } { 3 },$ then the rate of change of the area in cm2/min is

Accepted Answer

A) -4 
B) -8 
C) -16 
D) -32 
E) -64 
A) -4 
B) -8 
C) -16 
D) -32 
E) -64

Question 5

Let $s ^ { 2 } = x ^ { 2 } + 9$ If $\frac { d x } { d t } = 4$ when $x = 4 ,$ then $\frac { d s } { d t }$ is

Accepted Answer

A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 1 } { 5 }$ 
C) 5 
D)  $\frac { 16 } { 5 }$ 
E) 16 
A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 1 } { 5 }$ 
C) 5 
D)  $\frac { 16 } { 5 }$ 
E) 16

Question 6

Let $y = f ( x )$ be a differentiable function for which the graph of its derivative, ƒ ', is given below:
On what interval(s) is the graph of f decreasing?

Accepted Answer

A)  $( - \infty , 1 )$ 
B)  $( - \infty , - 2 ) \cup ( 0 , \infty )$ 
C) (-2, 0) 
D)  $( 1 , \infty )$ 
E) (-2, 1) 
A)  $( - \infty , 1 )$ 
B)  $( - \infty , - 2 ) \cup ( 0 , \infty )$ 
C) (-2, 0) 
D)  $( 1 , \infty )$ 
E) (-2, 1)

Question 7

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ on $[ - 2,2 ]$ The absolute minimum and maximum of ƒare located respectively at x =

Accepted Answer

A) -2,2 
B) -1,2 
C)  $- \frac { 1 } { 3 } , 2$ 
D)  $- 2,1$ 
E)  $- \frac { 1 } { 3 } , 1$ 
A) -2,2 
B) -1,2 
C)  $- \frac { 1 } { 3 } , 2$ 
D)  $- 2,1$ 
E)  $- \frac { 1 } { 3 } , 1$

Question 8

Let $V = \frac { 3 } { 16 } \pi h ^ { 3 }$ If $\frac { d V } { d t } = - 72$ when $h = 12$ then $\frac { d h } { d t }$ is

Accepted Answer

A)  $\frac { 4 } { 3 \pi }$ 
B)  $\frac { 8 } { 3 \pi }$ 
C)  $- \frac { 8 } { 3 \pi }$ 
D)  $\frac { 8 } { 9 \pi }$ 
E)  $- \frac { 8 } { 9 \pi }$ 
A)  $\frac { 4 } { 3 \pi }$ 
B)  $\frac { 8 } { 3 \pi }$ 
C)  $- \frac { 8 } { 3 \pi }$ 
D)  $\frac { 8 } { 9 \pi }$ 
E)  $- \frac { 8 } { 9 \pi }$

Question 9

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ Then ƒ has a relative maximum at x =

Accepted Answer

A)  $- \frac { 1 } { 3 }$ 
B) 1 
C)  $\frac { 1 } { 3 }$ 
D) -1 
E) 2 
A)  $- \frac { 1 } { 3 }$ 
B) 1 
C)  $\frac { 1 } { 3 }$ 
D) -1 
E) 2

Question 10

A spherical balloon is inflated at the rate of 10 m3/min when the radius is 3 m. The rate of increase of the surface area of the balloon is

Accepted Answer

A)  $\frac { 80 } { 3 }$ 
B)  $\frac { 40 } { 3 }$ 
C)  $\frac { 20 } { 3 }$ 
D)  $\frac { 20 } { 3 }$. 
E)  $\frac { 5 } { 3 }$ 
A)  $\frac { 80 } { 3 }$ 
B)  $\frac { 40 } { 3 }$ 
C)  $\frac { 20 } { 3 }$ 
D)  $\frac { 20 } { 3 }$. 
E)  $\frac { 5 } { 3 }$

Question 11

Determine which of the following is not true for the graph of $f ( x ) = \frac { x ^ { 2 } - 1 } { x - 1 }$

Accepted Answer

A) ƒ has no relative maximum. 
B) ƒ has no relative minimum. 
C) ƒ has a vertical asymptote: x = 1. 
D) ƒ has no horizontal asymptote. 
E) ƒ is discontinuous on $( - \infty , \infty )$ 
A) ƒ has no relative maximum. 
B) ƒ has no relative minimum. 
C) ƒ has a vertical asymptote: x = 1. 
D) ƒ has no horizontal asymptote. 
E) ƒ is discontinuous on $( - \infty , \infty )$

Question 12

Determine which of the following is not true for the graph of $f ( x ) = x ^ { \frac { 1 } { 3 } }$

Accepted Answer

A) ƒ is continuous on $( - \infty , \infty ) .$ 
B) ƒ has no relative maximum. 
C) ƒ has no relative minimum. 
D) ƒ does not have a point of inflection at x = 0. 
E) ƒ is concave downward on $( - \infty , 0 )$ 
A) ƒ is continuous on $( - \infty , \infty ) .$ 
B) ƒ has no relative maximum. 
C) ƒ has no relative minimum. 
D) ƒ does not have a point of inflection at x = 0. 
E) ƒ is concave downward on $( - \infty , 0 )$

Question 13

Determine the value of the limit $\lim _ { x \rightarrow 0 } \frac { \ln ( \sec x ) } { x ^ { 2 } }$ ?

Accepted Answer

A)  $- \infty$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) 0 
E)  $\infty$ 
A)  $- \infty$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 2 }$ 
D) 0 
E)  $\infty$

Question 14

Let $f ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 x$ Then ƒ has a point of inflection at x =

Accepted Answer

A)  $- \frac { 1 } { 3 }$ 
B) 1 
C)  $\frac { 1 } { 3 }$ 
D) -1 
E) 3 
A)  $- \frac { 1 } { 3 }$ 
B) 1 
C)  $\frac { 1 } { 3 }$ 
D) -1 
E) 3

Question 15

A cardboard poster containing 32 square inches of printed region is to have a margin of 2 inches at the top and bottom and 0.75 inch at the sides. The dimensions of the smallest piece of cardboard that can be used to make the poster are

Accepted Answer

A)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 3 }$ in by $\frac { 3 + 4 \sqrt { 3 } } { 2 }$ in 
B)  $\frac { 5 ( 3 + 4 \sqrt { 3 } ) } { 3 }$  in by $\frac { 3 + 4 \sqrt { 3 } } { 2 }$ ?in 
C)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 3 }$ in by $\frac { 3 + 4 \sqrt { 3 } } { 3 }$ in 
D)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 2 }$  in by $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 2 }$ in 
E)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 3 }$  in by $\frac { 3 + 4 \sqrt { 3 } } { 4 }$in 
A)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 3 }$ in by $\frac { 3 + 4 \sqrt { 3 } } { 2 }$ in 
B)  $\frac { 5 ( 3 + 4 \sqrt { 3 } ) } { 3 }$  in by $\frac { 3 + 4 \sqrt { 3 } } { 2 }$ ?in 
C)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 3 }$ in by $\frac { 3 + 4 \sqrt { 3 } } { 3 }$ in 
D)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 2 }$  in by $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 2 }$ in 
E)  $\frac { 4 ( 3 + 4 \sqrt { 3 } ) } { 3 }$  in by $\frac { 3 + 4 \sqrt { 3 } } { 4 }$in

Question 16

Let $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 1$ The set of all critical numbers of ƒ is

Accepted Answer

A)  $\left\{ 0 , - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ 0 , \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ 1 , - \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ 1 , \frac { 3 } { 2 } \right\}$ 
E)  $\{ 0,2 \}$ 
A)  $\left\{ 0 , - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ 0 , \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ 1 , - \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ 1 , \frac { 3 } { 2 } \right\}$ 
E)  $\{ 0,2 \}$

Question 17

Let $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 3 } { 2 } x ^ { 2 } + 8$ Then ƒ has a point of inflection at x =

Accepted Answer

A)  $\pm \frac { 1 } { 2 }$ 
B)  $\pm 1$ 
C)  $\pm \frac { 1 } { 3 }$ 
D)  $\pm \frac { 3 } { 2 }$ 
E)  $\pm \frac { 5 } { 2 }$ 
A)  $\pm \frac { 1 } { 2 }$ 
B)  $\pm 1$ 
C)  $\pm \frac { 1 } { 3 }$ 
D)  $\pm \frac { 3 } { 2 }$ 
E)  $\pm \frac { 5 } { 2 }$

Question 18

Let $f ( x ) = x ^ { 3 } + 4 x + 1$ Then ƒ has a point of inflection at x =

Accepted Answer

A) -3 
B) -2 
C) -1 
D) 0 
E) 2 
A) -3 
B) -2 
C) -1 
D) 0 
E) 2

Question 19

Let $\sin ^ { 2 } x + \cos ^ { 2 } y = \frac { 5 } { 4 }$ If $\frac { d y } { d t } = - \frac { \sqrt { 3 } } { 2 }$ when $x = \frac { 2 \pi } { 3 }$ and $y = \frac { 3 \pi } { 4 },$ then $\frac { d x } { d t }$ is

Accepted Answer

A) -1 
B)  $- \frac { 1 } { 2 }$ 
C) 1 
D)  $\frac { 1 } { 2 }$ 
E)  $\frac { 3 } { 2 }$ 
A) -1 
B)  $- \frac { 1 } { 2 }$ 
C) 1 
D)  $\frac { 1 } { 2 }$ 
E)  $\frac { 3 } { 2 }$

Question 20

Let $f ( x ) = x ^ { 2 } - 3 x \text { on } [ 0,3 ]$ on $[ 0,3 ]$ . Then the set of all c in (0,3) guaranteed by Rolle's Theorem is

Accepted Answer

A)  $\{ - 3 \}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
E)  $\left\{ \frac { 3 } { 2 } \right\}$ 
A)  $\{ - 3 \}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } \right\}$ 
E)  $\left\{ \frac { 3 } { 2 } \right\}$

Let $f ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 x - \frac { 1 } { 5 }$ The set of all critical numbers of ƒ is

Let $A = ( 10 + x ) ^ { 2 }$ If $\frac { d x } { d t } = \frac { 2 } { 15 }$ when then $\frac { d A } { d t }$ is

The antiderivative of $f ( x ) = 6 - 3 x ^ { - 4 }$ is

An isosceles triangle has equal sides 4 cm long and the included angle ?. If $\frac { d \theta } { d t } = 2 \mathrm { rad } / \mathrm { min }$ when $\theta = \frac { \pi } { 3 },$ then the rate of change of the area in cm²/min is

Let $s ^ { 2 } = x ^ { 2 } + 9$ If $\frac { d x } { d t } = 4$ when $x = 4 ,$ then $\frac { d s } { d t }$ is

Let $y = f ( x )$ be a differentiable function for which the graph of its derivative, ƒ ', is given below: On what interval(s) is the graph of f decreasing?

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ on $[ - 2,2 ]$ The absolute minimum and maximum of ƒare located respectively at x =

Let $V = \frac { 3 } { 16 } \pi h ^ { 3 }$ If $\frac { d V } { d t } = - 72$ when $h = 12$ then $\frac { d h } { d t }$ is

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ Then ƒ has a relative maximum at x =

A spherical balloon is inflated at the rate of 10 m³/min when the radius is 3 m. The rate of increase of the surface area of the balloon is

Determine which of the following is not true for the graph of $f ( x ) = \frac { x ^ { 2 } - 1 } { x - 1 }$

Determine which of the following is not true for the graph of $f ( x ) = x ^ { \frac { 1 } { 3 } }$

Determine the value of the limit $\lim _ { x \rightarrow 0 } \frac { \ln ( \sec x ) } { x ^ { 2 } }$ ?

Let $f ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 x$ Then ƒ has a point of inflection at x =

A cardboard poster containing 32 square inches of printed region is to have a margin of 2 inches at the top and bottom and 0.75 inch at the sides. The dimensions of the smallest piece of cardboard that can be used to make the poster are

Let $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 1$ The set of all critical numbers of ƒ is

Let $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 3 } { 2 } x ^ { 2 } + 8$ Then ƒ has a point of inflection at x =

Let $f ( x ) = x ^ { 3 } + 4 x + 1$ Then ƒ has a point of inflection at x =

Let $\sin ^ { 2 } x + \cos ^ { 2 } y = \frac { 5 } { 4 }$ If $\frac { d y } { d t } = - \frac { \sqrt { 3 } } { 2 }$ when $x = \frac { 2 \pi } { 3 }$ and $y = \frac { 3 \pi } { 4 },$ then $\frac { d x } { d t }$ is

Let $f ( x ) = x ^ { 2 } - 3 x \text { on } [ 0,3 ]$ on $[ 0,3 ]$ . Then the set of all c in (0,3) guaranteed by Rolle's Theorem is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

The Integral

Applications of the Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Exam 5: Applications of the Derivative

Let f(x)=15x3−95x2+3x−15f ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 x - \frac { 1 } { 5 }f(x)=51​x3−59​x2+3x−51​ The set of all critical numbers of ƒ is

Let A=(10+x)2A = ( 10 + x ) ^ { 2 }A=(10+x)2 If dxdt=215\frac { d x } { d t } = \frac { 2 } { 15 }dtdx​=152​ when then dAdt\frac { d A } { d t }dtdA​ is

The antiderivative of f(x)=6−3x−4f ( x ) = 6 - 3 x ^ { - 4 }f(x)=6−3x−4 is

An isosceles triangle has equal sides 4 cm long and the included angle ?. If dθdt=2rad/min\frac { d \theta } { d t } = 2 \mathrm { rad } / \mathrm { min }dtdθ​=2rad/min when θ=π3,\theta = \frac { \pi } { 3 },θ=3π​, then the rate of change of the area in cm2/min is

Let s2=x2+9s ^ { 2 } = x ^ { 2 } + 9s2=x2+9 If dxdt=4\frac { d x } { d t } = 4dtdx​=4 when x=4,x = 4 ,x=4, then dsdt\frac { d s } { d t }dtds​ is

Let y=f(x)y = f ( x )y=f(x) be a differentiable function for which the graph of its derivative, ƒ ', is given below: On what interval(s) is the graph of f decreasing?

Let f(x)=x3−x2−x+8f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8f(x)=x3−x2−x+8 on [−2,2][ - 2,2 ][−2,2] The absolute minimum and maximum of ƒare located respectively at x =

Let V=316πh3V = \frac { 3 } { 16 } \pi h ^ { 3 }V=163​πh3 If dVdt=−72\frac { d V } { d t } = - 72dtdV​=−72 when h=12h = 12h=12 then dhdt\frac { d h } { d t }dtdh​ is

Let f(x)=x3−x2−x+8f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8f(x)=x3−x2−x+8 Then ƒ has a relative maximum at x =

A spherical balloon is inflated at the rate of 10 m3/min when the radius is 3 m. The rate of increase of the surface area of the balloon is

Determine which of the following is not true for the graph of f(x)=x2−1x−1f ( x ) = \frac { x ^ { 2 } - 1 } { x - 1 }f(x)=x−1x2−1​

Determine which of the following is not true for the graph of f(x)=x13f ( x ) = x ^ { \frac { 1 } { 3 } }f(x)=x31​

Determine the value of the limit lim⁡x→0ln⁡(sec⁡x)x2\lim _ { x \rightarrow 0 } \frac { \ln ( \sec x ) } { x ^ { 2 } }limx→0​x2ln(secx)​ ?

Let f(x)=15x3−95x2+3xf ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 xf(x)=51​x3−59​x2+3x Then ƒ has a point of inflection at x =

A cardboard poster containing 32 square inches of printed region is to have a margin of 2 inches at the top and bottom and 0.75 inch at the sides. The dimensions of the smallest piece of cardboard that can be used to make the poster are

Let f(x)=x4−2x3+1f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 1f(x)=x4−2x3+1 The set of all critical numbers of ƒ is

Let f(x)=14x4−32x2+8f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 3 } { 2 } x ^ { 2 } + 8f(x)=41​x4−23​x2+8 Then ƒ has a point of inflection at x =

Let f(x)=x3+4x+1f ( x ) = x ^ { 3 } + 4 x + 1f(x)=x3+4x+1 Then ƒ has a point of inflection at x =

Let f(x)=x2−3x on [0,3]f ( x ) = x ^ { 2 } - 3 x \text { on } [ 0,3 ]f(x)=x2−3x on [0,3] on [0,3][ 0,3 ][0,3] . Then the set of all c in (0,3) guaranteed by Rolle's Theorem is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

The Integral

Applications of the Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Let $f ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 x - \frac { 1 } { 5 }$ The set of all critical numbers of ƒ is

Let $A = ( 10 + x ) ^ { 2 }$ If $\frac { d x } { d t } = \frac { 2 } { 15 }$ when then $\frac { d A } { d t }$ is

The antiderivative of $f ( x ) = 6 - 3 x ^ { - 4 }$ is

An isosceles triangle has equal sides 4 cm long and the included angle ?. If $\frac { d \theta } { d t } = 2 \mathrm { rad } / \mathrm { min }$ when $\theta = \frac { \pi } { 3 },$ then the rate of change of the area in cm²/min is

Let $s ^ { 2 } = x ^ { 2 } + 9$ If $\frac { d x } { d t } = 4$ when $x = 4 ,$ then $\frac { d s } { d t }$ is

Let $y = f ( x )$ be a differentiable function for which the graph of its derivative, ƒ ', is given below: On what interval(s) is the graph of f decreasing?

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ on $[ - 2,2 ]$ The absolute minimum and maximum of ƒare located respectively at x =

Let $V = \frac { 3 } { 16 } \pi h ^ { 3 }$ If $\frac { d V } { d t } = - 72$ when $h = 12$ then $\frac { d h } { d t }$ is

Let $f ( x ) = x ^ { 3 } - x ^ { 2 } - x + 8$ Then ƒ has a relative maximum at x =

A spherical balloon is inflated at the rate of 10 m³/min when the radius is 3 m. The rate of increase of the surface area of the balloon is

Determine which of the following is not true for the graph of $f ( x ) = \frac { x ^ { 2 } - 1 } { x - 1 }$

Determine which of the following is not true for the graph of $f ( x ) = x ^ { \frac { 1 } { 3 } }$

Determine the value of the limit $\lim _ { x \rightarrow 0 } \frac { \ln ( \sec x ) } { x ^ { 2 } }$ ?

Let $f ( x ) = \frac { 1 } { 5 } x ^ { 3 } - \frac { 9 } { 5 } x ^ { 2 } + 3 x$ Then ƒ has a point of inflection at x =

Let $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 1$ The set of all critical numbers of ƒ is

Let $f ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 3 } { 2 } x ^ { 2 } + 8$ Then ƒ has a point of inflection at x =

Let $f ( x ) = x ^ { 3 } + 4 x + 1$ Then ƒ has a point of inflection at x =

Let $f ( x ) = x ^ { 2 } - 3 x \text { on } [ 0,3 ]$ on $[ 0,3 ]$ . Then the set of all c in (0,3) guaranteed by Rolle's Theorem is