Question 1

Sketch the graph of   on   and find its absolute maximum and absolute minimum values, if any.

Accepted Answer

Abs. max.

Question 2

The sum of two positive numbers is   . What is the smallest possible value of the sum of their squares?

Accepted Answer

The answer of The sum of two positive numbers is...

Question 3

Find the critical number(s), if any of the function

Accepted Answer

A) 0,   
B)    
C)    
D) 0,   
A) 0,   
B)    
C)    
D) 0,   A

Question 4

Find the critical numbers of   .

Accepted Answer

A) 0, 3,   
B) 0, 3,   
C)    
D) 0, 2,   
E) 0, 2,   
A) 0, 3,   
B) 0, 3,   
C)    
D) 0, 2,   
E) 0, 2,

Question 5

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

Accepted Answer

A) 4.35 m 
B) 3.25 m 
C) 0 m 
D) 5.35 m 
E) 4.4 m 
A) 4.35 m 
B) 3.25 m 
C) 0 m 
D) 5.35 m 
E) 4.4 m

Question 6

Determine where the graph of   is concave upward and where it is concave downward. Also, find all inflection points of the function.

Accepted Answer

concave upward: @#IMG-DLM& and

Question 7

Find the most general antiderivative of the function.

Accepted Answer

The answer of Find the most general antiderivative of the...

Question 8

Use Newton's method with the specified initial approximation   to find   , the third approximation to the root of the given equation. (Give your answer to four decimal places.)

Accepted Answer

The answer of Use Newton's method with the specified initial...

Question 9

Use Newton's method with the specified initial approximation   to find   , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Find the absolute maximum and absolute minimum values, if any, of the function   on   .

Accepted Answer

A) Abs. max.   abs. min.   
B) Abs. max.   abs. min.   
C) Abs. max.   abs. min.   
D) Abs. max.   abs. min.   
A) Abs. max.   abs. min.   
B) Abs. max.   abs. min.   
C) Abs. max.   abs. min.   
D) Abs. max.   abs. min.

Question 11

Find the position function of a particle moving along a coordinate line that satisfies the given condition.   , s(1) = -1

Accepted Answer

The answer of Find the position function of a particle...

Question 12

Find the maximum and minimum points of the function.

Accepted Answer

The answer of Find the maximum and minimum points of...

Question 13

The graph of the derivative   of a continuous function f is shown. On what intervals is f decreasing?   .

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 14

A car braked with a constant deceleration of 40   , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Accepted Answer

The answer of A car braked with a constant deceleration...

Question 15

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval.   ,

Accepted Answer

A)    
B)    
C)      
D)    
E) None of these 
A)    
B)    
C)      
D)    
E) None of these

Question 16

The function   satisfies the hypotheses of Rolle's Theorem on the interval   . Find all values of c that satisfy the conclusion of the theorem.

Accepted Answer

A) -6, -4 
B) -5, -4 
C) -6 
D) -5 
A) -6, -4 
B) -5, -4 
C) -6 
D) -5

Question 17

Find the critical number(s), if any, of the function

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

A woman at a point A on the shore of a circular lake with radius   wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of   and row a boat at   . How should she proceed? (Find   ). Round the result, if necessary, to the nearest hundredth.

Accepted Answer

A)    radians 
B) She should row from point A to point C radians 
C)    radians 
D)    radians 
E) She should walk around the lake from point A to point C. 
A)    radians 
B) She should row from point A to point C radians 
C)    radians 
D)    radians 
E) She should walk around the lake from point A to point C.

Question 19

Use the guidelines of this section to sketch the curve.   Select the graph of the curve.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Use Newton's method with the specified initial approximation   to find   , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Sketch the graph of on and find its absolute maximum and absolute minimum values, if any.

The sum of two positive numbers is . What is the smallest possible value of the sum of their squares?

Find the critical number(s), if any of the function

Find the critical numbers of .

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

Determine where the graph of is concave upward and where it is concave downward. Also, find all inflection points of the function.

Find the most general antiderivative of the function.

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

Find the absolute maximum and absolute minimum values, if any, of the function on .

Find the position function of a particle moving along a coordinate line that satisfies the given condition. , s(1) = -1

Find the maximum and minimum points of the function.

The graph of the derivative of a continuous function f is shown. On what intervals is f decreasing? .

A car braked with a constant deceleration of 40 , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. ,

The function satisfies the hypotheses of Rolle's Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.

Find the critical number(s), if any, of the function

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 4: Applications of Differentiation

Sketch the graph of on and find its absolute maximum and absolute minimum values, if any.

The sum of two positive numbers is . What is the smallest possible value of the sum of their squares?

Find the critical number(s), if any of the function

Find the critical numbers of .

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

Determine where the graph of is concave upward and where it is concave downward. Also, find all inflection points of the function.

Find the most general antiderivative of the function.

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

Find the absolute maximum and absolute minimum values, if any, of the function on .

Find the position function of a particle moving along a coordinate line that satisfies the given condition. , s(1) = -1

Find the maximum and minimum points of the function.

The graph of the derivative of a continuous function f is shown. On what intervals is f decreasing? .

A car braked with a constant deceleration of 40 , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. ,

The function satisfies the hypotheses of Rolle's Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.

Find the critical number(s), if any, of the function

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters