Question 1

If f(x) = 4x4 -17x3 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 2

The position function of a particle is given by s(t) = 3t + sin 5t. Find the acceleration function.

Accepted Answer

The answer of The position function of a particle is...

Question 3

Answer true or false. Every function has an absolute maximum and an absolute minimum if its domain is restricted to where f is defined on an interval [-a, a], where a is finite.

Accepted Answer

A) True 
 B)False

Question 4

The largest interval over which f is increasing for f(x) = (x - 2)6 is

Accepted Answer

A)  [-2, 2] 
B)  [2, $\infty$) 
C)  (-$\infty$ , -2] 
D)  (-$\infty$ , 2] 
E)  [-2, $\infty$) 
A)  [-2, 2] 
B)  [2, $\infty$) 
C)  (-$\infty$ , -2] 
D)  (-$\infty$ , 2] 
E)  [-2, $\infty$)

Question 5

Given   . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-5, 1].

Accepted Answer

Absolute maximum of

Question 6

Answer true or false. All functions of the form f(x) = axn , where n is odd and a $\neq$0 have an inflection point.

Accepted Answer

A) True 
 B)False

Question 7

Sketch the graph of y = x3 + 12x2. Find any minima, maxima, and inflection points.

Accepted Answer

y' = 3x² + 24x y'' = 6x + 24 Re

Question 8

f(x) = sin21.35x on 0 < x < 2 $\pi$ has

Accepted Answer

A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  neither a relative maximum nor a relative minimum 
E)  cannot be determined 
A)  a relative maximum only 
B)  a relative minimum only 
C)  both a relative maximum and a relative minimum 
D)  neither a relative maximum nor a relative minimum 
E)  cannot be determined

Question 9

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x7

Accepted Answer

@#IMG-DLM& = 1 f '(x) = 7x⁶ 7x⁶

Question 10

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in3 and requires a minimum amount of cardboard. Find the most economical dimensions.

Accepted Answer

Let x and y be the dimensions shown in t

Question 11

A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side. Two kinds of fencing will be used with heavy duty fencing selling for $5 a foot on the side opposite the wall. The two remaining sides will use standard fencing selling for $4 a foot. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $55,200?

Accepted Answer

x = 5,520

Question 12

If f(x) = sin 6x (0,  $\pi$/3), find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing (0,  @#LAT-DLM&/12)

Question 13

s(t) = t5 - 10, t   0. Find s when a = 0.

Accepted Answer

A)   20 
B)   -20 
C)   10 
D)   -10 
E)   0 
A)   20 
B)   -20 
C)   10 
D)   -10 
E)   0

Question 14

The derivative of a continuous function is f '(x) = 4(x -5)2(4x + 2). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

Accepted Answer

Critical points are x = 5 and

Question 15

Verify that f(x) = x3- x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

Accepted Answer

f(-1) = f(1) = 0
f '

Question 16

Find the value c that satisfies the Mean-Value Theorem for f(x) = x3 on [0, 2].

Accepted Answer

A)    
B)    
C)  2 
D)  0 
E)    
A)    
B)    
C)  2 
D)  0 
E)

Question 17

Given the position function s = 3t3 - 18t2 ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Accepted Answer

v = 9t² - 36t a = 1

Question 18

The equation, x3 + x2 - 5x - 6 = 0 has one real solution for 1 < x < 6. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

Accepted Answer

f(x) = x³+x

Question 19

Find the relative extrema for f(x) = 3x2 - 12x + 8.

Accepted Answer

f '(x) = 6x - 12
Critical poin

Question 20

Find values for x and y such that their product is a minimum if y = 5x -6.

Accepted Answer

Let x = one number and y = oth

If f(x) = 4x⁴ -17x³ , find the intervals where f is increasing and where f is decreasing.

The position function of a particle is given by s(t) = 3t + sin 5t. Find the acceleration function.

Answer true or false. Every function has an absolute maximum and an absolute minimum if its domain is restricted to where f is defined on an interval [-a, a], where a is finite.

The largest interval over which f is increasing for f(x) = (x - 2)⁶ is

Given . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-5, 1].

Answer true or false. All functions of the form f(x) = axⁿ , where n is odd and a $\neq$ 0 have an inflection point.

Sketch the graph of y = x³ + 12x². Find any minima, maxima, and inflection points.

f(x) = sin²1.35x on 0 < x < 2 $\pi$ has

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x⁷

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in³ and requires a minimum amount of cardboard. Find the most economical dimensions.

If f(x) = sin 6x (0, $\pi$ /3), find the intervals where f is increasing and where f is decreasing.

s(t) = t⁵ - 10, t 0. Find s when a = 0.

The derivative of a continuous function is f '(x) = 4(x -5)²(4x + 2). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

Verify that f(x) = x³- x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

Find the value c that satisfies the Mean-Value Theorem for f(x) = x³ on [0, 2].

Given the position function s = 3t³ - 18t² ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

The equation, x³ + x²- 5x - 6 = 0 has one real solution for 1 < x < 6. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

Find the relative extrema for f(x) = 3x² - 12x + 8.

Find values for x and y such that their product is a minimum if y = 5x -6.

Limits and Continuity

The Derivative

Topics in Deifferentiation

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 4: The Derivative in Graphing and Applications

If f(x) = 4x4 -17x3 , find the intervals where f is increasing and where f is decreasing.

The position function of a particle is given by s(t) = 3t + sin 5t. Find the acceleration function.

Answer true or false. Every function has an absolute maximum and an absolute minimum if its domain is restricted to where f is defined on an interval [-a, a], where a is finite.

The largest interval over which f is increasing for f(x) = (x - 2)6 is

Given . Use a graphing utility to estimate the absolute maximum and minimum values of f, if any, on the interval [-5, 1].

Answer true or false. All functions of the form f(x) = axn , where n is odd and a ≠\neq= 0 have an inflection point.

Sketch the graph of y = x3 + 12x2. Find any minima, maxima, and inflection points.

f(x) = sin21.35x on 0 < x < 2 π\piπ has

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x7

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in3 and requires a minimum amount of cardboard. Find the most economical dimensions.

If f(x) = sin 6x (0, π\piπ /3), find the intervals where f is increasing and where f is decreasing.

s(t) = t5 - 10, t 0. Find s when a = 0.

The derivative of a continuous function is f '(x) = 4(x -5)2(4x + 2). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

Verify that f(x) = x3- x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

Find the value c that satisfies the Mean-Value Theorem for f(x) = x3 on [0, 2].

Given the position function s = 3t3 - 18t2 ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

The equation, x3 + x2 - 5x - 6 = 0 has one real solution for 1 < x < 6. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

Find the relative extrema for f(x) = 3x2 - 12x + 8.

Find values for x and y such that their product is a minimum if y = 5x -6.

Limits and Continuity

The Derivative

Topics in Deifferentiation

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

If f(x) = 4x⁴ -17x³ , find the intervals where f is increasing and where f is decreasing.

The largest interval over which f is increasing for f(x) = (x - 2)⁶ is

Answer true or false. All functions of the form f(x) = axⁿ , where n is odd and a $\neq$ 0 have an inflection point.

Sketch the graph of y = x³ + 12x². Find any minima, maxima, and inflection points.

f(x) = sin²1.35x on 0 < x < 2 $\pi$ has

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x⁷

An open-top shipping crate with square bottom and rectangular sides is to hold 108 in³ and requires a minimum amount of cardboard. Find the most economical dimensions.

If f(x) = sin 6x (0, $\pi$ /3), find the intervals where f is increasing and where f is decreasing.

s(t) = t⁵ - 10, t 0. Find s when a = 0.

The derivative of a continuous function is f '(x) = 4(x -5)²(4x + 2). Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

Verify that f(x) = x³- x satisfies the hypothesis of Rolle's Theorem on the interval [-1, 1] and find all values of C in (-1, 1) such that f '(C) = 0

Find the value c that satisfies the Mean-Value Theorem for f(x) = x³ on [0, 2].

Given the position function s = 3t³ - 18t² ; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

The equation, x³ + x²- 5x - 6 = 0 has one real solution for 1 < x < 6. Approximate it by Newton's Method. Use 3 for your initial value and calculate eight iterations.

Find the relative extrema for f(x) = 3x² - 12x + 8.