Question 1

Find the equation of the tangent line to the graph of $f ( x ) = x ^ { 2 } + 3$ at the point (3,12).

Accepted Answer

A) y = 12 
B) y = 6x - 6 
C) x = 3 
D) Not defined 
A) y = 12 
B) y = 6x - 6 
C) x = 3 
D) Not defined

Question 2

Find $\frac { d y } { d x }$ ,where $$x y ^ { 3 } - 3 x ^ { 2 } = 7 y$$ .

Accepted Answer

A)  $$\frac { 6 x - y ^ { 3 } } { 3 x y ^ { 2 } - 7 }$$ 
B)  $y ^ { 3 } - 6 x$ 
C)  $\frac { 6 x ^ { 2 } } { y ^ { 3 } }$ 
D)  $y ^ { 3 } - 6 x - 7$ 
A)  $$\frac { 6 x - y ^ { 3 } } { 3 x y ^ { 2 } - 7 }$$ 
B)  $y ^ { 3 } - 6 x$ 
C)  $\frac { 6 x ^ { 2 } } { y ^ { 3 } }$ 
D)  $y ^ { 3 } - 6 x - 7$

Question 3

Find the equation of the tangent line to the given curve at the specified point. $$x ^ { 5 } y ^ { 5 } - 5 x y = 6 x + y - 8$$ ; (0,8)

Accepted Answer

A)  $y = - \frac { 1 } { 46 } x + 8$ 
B) y = -46x + 8 
C) y = 46x + 8 
D)  $y = \frac { 1 } { 46 } x + 8$ 
A)  $y = - \frac { 1 } { 46 } x + 8$ 
B) y = -46x + 8 
C) y = 46x + 8 
D)  $y = \frac { 1 } { 46 } x + 8$

Question 4

Find all points on the graph of the function $f ( x ) = \frac { x ^ { 2 } } { x + 2 }$ where the tangent line is horizontal.

Accepted Answer

A) (0,0)and (-4,-8) 
B) There are none. 
C) (0,0) 
D) (2,1) 
A) (0,0)and (-4,-8) 
B) There are none. 
C) (0,0) 
D) (2,1)

Find the equation of the tangent line to the graph of $f ( x ) = x ^ { 2 } + 3$ at the point (3,12).

Find $\frac { d y } { d x }$ ,where $x y ^ { 3 } - 3 x ^ { 2 } = 7 y$ .

Find the equation of the tangent line to the given curve at the specified point. $x ^ { 5 } y ^ { 5 } - 5 x y = 6 x + y - 8$ ; (0,8)

Find all points on the graph of the function $f ( x ) = \frac { x ^ { 2 } } { x + 2 }$ where the tangent line is horizontal.

Functions,graphs,and Limits

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Exam 2: Differentiation: Basic Concepts

Find the equation of the tangent line to the graph of f(x)=x2+3f ( x ) = x ^ { 2 } + 3f(x)=x2+3 at the point (3,12).

Find dydx\frac { d y } { d x }dxdy​ ,where xy3−3x2=7yx y ^ { 3 } - 3 x ^ { 2 } = 7 yxy3−3x2=7y .

Find the equation of the tangent line to the given curve at the specified point. x5y5−5xy=6x+y−8x ^ { 5 } y ^ { 5 } - 5 x y = 6 x + y - 8x5y5−5xy=6x+y−8 ; (0,8)

Find all points on the graph of the function f(x)=x2x+2f ( x ) = \frac { x ^ { 2 } } { x + 2 }f(x)=x+2x2​ where the tangent line is horizontal.

Functions,graphs,and Limits

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Find the equation of the tangent line to the graph of $f ( x ) = x ^ { 2 } + 3$ at the point (3,12).

Find $\frac { d y } { d x }$ ,where $x y ^ { 3 } - 3 x ^ { 2 } = 7 y$ .

Find the equation of the tangent line to the given curve at the specified point. $x ^ { 5 } y ^ { 5 } - 5 x y = 6 x + y - 8$ ; (0,8)

Find all points on the graph of the function $f ( x ) = \frac { x ^ { 2 } } { x + 2 }$ where the tangent line is horizontal.