Question 1

Find   in terms of x and y given that   . Use the original equation to simplify your answer. ​

Accepted Answer

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Question 2

Find an equation of the tangent line to the graph of the function   at the point   . ​

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Question 3

Find the derivative of the function. ​   ​

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Question 4

Find the derivative of the function   . ​

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Question 5

Use logarithmic differentiation to find   . ​   ​

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Question 6

Find   by implicit differentiation. ​   ​

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Question 7

Evaluate the derivative of the function at the given point. ​   ,   ​

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Question 8

A ladder 25 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 2 feet per second. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changed when the base of the ladder is 11 feet from the wall. Round your answer to two decimal places. ​   ​

Accepted Answer

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Question 9

Find the derivative of the following function using the limiting process. ​   ​

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Question 10

Find the derivative of the function   . Simplify your answer. ​

Accepted Answer

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Question 11

Find an equation to the tangent line to the graph of the function   at the point   . The coefficients below are given to two decimal places. ​

Accepted Answer

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Question 12

A manufacturer of digital audio players estimates that the profit for selling a particular model is   ,   where P is the profit in dollars and x is the advertising expense in 10,000's of dollars (see figure). Find the smaller of two advertising amounts that yield a profit P of $2,100,000. Round your answer to the nearest dollar. ​   ​

Accepted Answer

A)  $460,892 
B)  $315,369 
C)  $363,471 
D)  $512,458 
E)  $384,356 
A)  $460,892 
B)  $315,369 
C)  $363,471 
D)  $512,458 
E)  $384,356

Question 13

Find   by implicit differentiation. ​   ​

Accepted Answer

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Question 14

A population of 350 bacteria is introduced into a culture and grows in number according to the equation   where t is measured in hours. Find the rate at which the population is growing when   . Round your answer to two decimal places. ​

Accepted Answer

A)  125.07 bacteria per hour 
B)  32.81 bacteria per hour 
C)  27.63 bacteria per hour 
D)  16.00 bacteria per hour 
E)  28.71 bacteria per hour 
A)  125.07 bacteria per hour 
B)  32.81 bacteria per hour 
C)  27.63 bacteria per hour 
D)  16.00 bacteria per hour 
E)  28.71 bacteria per hour

Question 15

The ordering and transportation cost C for the components used in manufacturing a product is   ,   where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for   . Round your answer to two decimal places. ​

Accepted Answer

A)  -6.20 thousand dollars per hundred 
B)  7.41 thousand dollars per hundred 
C)  3.13 thousand dollars per hundred 
D)  -5.03 thousand dollars per hundred 
E)  -8.02 thousand dollars per hundred 
A)  -6.20 thousand dollars per hundred 
B)  7.41 thousand dollars per hundred 
C)  3.13 thousand dollars per hundred 
D)  -5.03 thousand dollars per hundred 
E)  -8.02 thousand dollars per hundred

Question 16

A buoy oscillates in simple harmonic motion   as waves move past it. The buoy moves a total of   feet (vertically) between its low point and its high point. It returns to its high point every   seconds. Determine the velocity of the buoy as a function of t. ​

Accepted Answer

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Question 17

Find the second derivative of the function. ​   ​

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Question 18

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. ​   ​

Accepted Answer

A)    
B)    and   
C)    and   
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E)  The graph has no horizontal tangents. 
A)    
B)    and   
C)    and   
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E)  The graph has no horizontal tangents.

Question 19

Find an equation of the tangent line to the graph of   at the point (1,0). ​

Accepted Answer

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Question 20

Find the slope of the graph of the function at the given value. ​   when   ​

Accepted Answer

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Find in terms of x and y given that . Use the original equation to simplify your answer.

Find an equation of the tangent line to the graph of the function at the point .

Find the derivative of the function.

Find the derivative of the function .

Use logarithmic differentiation to find .

Find by implicit differentiation.

Evaluate the derivative of the function at the given point. ,

Find the derivative of the following function using the limiting process.

Find the derivative of the function . Simplify your answer.

Find an equation to the tangent line to the graph of the function at the point . The coefficients below are given to two decimal places.

Find by implicit differentiation.

A population of 350 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours. Find the rate at which the population is growing when . Round your answer to two decimal places.

The ordering and transportation cost C for the components used in manufacturing a product is , where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for . Round your answer to two decimal places.

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of feet (vertically) between its low point and its high point. It returns to its high point every seconds. Determine the velocity of the buoy as a function of t.

Find the second derivative of the function.

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.

Find an equation of the tangent line to the graph of at the point (1,0).

Find the slope of the graph of the function at the given value. when

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 3: Differentiation

Find in terms of x and y given that . Use the original equation to simplify your answer. ​

Find an equation of the tangent line to the graph of the function at the point . ​

Find the derivative of the function. ​ ​

Find the derivative of the function . ​

Use logarithmic differentiation to find . ​ ​

Find by implicit differentiation. ​ ​

Evaluate the derivative of the function at the given point. ​ , ​

Find the derivative of the following function using the limiting process. ​ ​

Find the derivative of the function . Simplify your answer. ​

Find an equation to the tangent line to the graph of the function at the point . The coefficients below are given to two decimal places. ​

Find by implicit differentiation. ​ ​

A population of 350 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours. Find the rate at which the population is growing when . Round your answer to two decimal places. ​

The ordering and transportation cost C for the components used in manufacturing a product is , where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for . Round your answer to two decimal places. ​

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of feet (vertically) between its low point and its high point. It returns to its high point every seconds. Determine the velocity of the buoy as a function of t. ​

Find the second derivative of the function. ​ ​

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. ​ ​

Find an equation of the tangent line to the graph of at the point (1,0). ​

Find the slope of the graph of the function at the given value. ​ when ​

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find in terms of x and y given that . Use the original equation to simplify your answer.

Find an equation of the tangent line to the graph of the function at the point .

Find the derivative of the function.

Find the derivative of the function .

Use logarithmic differentiation to find .

Find by implicit differentiation.

Evaluate the derivative of the function at the given point. ,

Find the derivative of the following function using the limiting process.

Find the derivative of the function . Simplify your answer.

Find an equation to the tangent line to the graph of the function at the point . The coefficients below are given to two decimal places.

Find by implicit differentiation.

A population of 350 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours. Find the rate at which the population is growing when . Round your answer to two decimal places.

The ordering and transportation cost C for the components used in manufacturing a product is , where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for . Round your answer to two decimal places.

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of feet (vertically) between its low point and its high point. It returns to its high point every seconds. Determine the velocity of the buoy as a function of t.

Find the second derivative of the function.

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.

Find an equation of the tangent line to the graph of at the point (1,0).

Find the slope of the graph of the function at the given value. when