Question 1

Find the point on the graph of the function   that is closest to the point   . Round all numerical values in your answer to four decimal places.

Accepted Answer

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

Question 2

Find the cubic function of the form   are real numbers, which satisfies the conditions given below.

Accepted Answer

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

Question 3

Use a graphing utility to graph the function   and locate the absolute extrema of the function on the interval   .

Accepted Answer

A) absolute minimum:   no absolute maximum 
B) absolute minimum:   no absolute maximum 
C) absolute maximum:   absolute minimum:   
D) absolute minimum:   absolute maximum:   
E) absolute minimum:   no absolute maximum 
A) absolute minimum:   no absolute maximum 
B) absolute minimum:   no absolute maximum 
C) absolute maximum:   absolute minimum:   
D) absolute minimum:   absolute maximum:   
E) absolute minimum:   no absolute maximum

Question 4

Suppose a manufacturer has determined that the total cost C of operating a factory is   where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.)

Accepted Answer

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

Question 5

Find the equation of the tangent line T to the graph of   at the given point

Accepted Answer

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

Question 6

Which of the following functions passes through the point   and satisfies   ?

Accepted Answer

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

Question 7

A rectangle is bounded by the x- and y-axes and the graph of   (see figure). What length and width should the rectangle have so that its area is a maximum?

Accepted Answer

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

Find the point on the graph of the function that is closest to the point . Round all numerical values in your answer to four decimal places.

Find the cubic function of the form are real numbers, which satisfies the conditions given below.

Use a graphing utility to graph the function and locate the absolute extrema of the function on the interval .

Suppose a manufacturer has determined that the total cost C of operating a factory is where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.)

Find the equation of the tangent line T to the graph of at the given point

Which of the following functions passes through the point and satisfies ?

A rectangle is bounded by the x- and y-axes and the graph of (see figure). What length and width should the rectangle have so that its area is a maximum?

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 6: Applications of Differentiation

Find the point on the graph of the function that is closest to the point . Round all numerical values in your answer to four decimal places.

Find the cubic function of the form are real numbers, which satisfies the conditions given below.

Use a graphing utility to graph the function and locate the absolute extrema of the function on the interval .

Suppose a manufacturer has determined that the total cost C of operating a factory is where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.)

Find the equation of the tangent line T to the graph of at the given point

Which of the following functions passes through the point and satisfies ?

A rectangle is bounded by the x- and y-axes and the graph of (see figure). What length and width should the rectangle have so that its area is a maximum?

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters