Question 1

Use the definition f'(x) =   to find the derivative at x.
-f(x) = 10 - 3x2

Accepted Answer

A)  10-3x 
B)  -6x 
C)  10-6x 
D)  -6x2 
A)  10-3x 
B)  -6x 
C)  10-6x 
D)  -6x2

Question 2

Provide an appropriate response.
-Find f'(x) if f(x) =π.

Accepted Answer

A)  f'x=0 
B)  f'(x)=1 
C)  f'x=π 
D)  f'(x) = π2 
A)  f'x=0 
B)  f'(x)=1 
C)  f'x=π 
D)  f'(x) = π2

Question 3

Provide an appropriate response.
-Find the values of x where the tangent line is horizontal for f(x) = 3x3 - 2x2 - 9.

Accepted Answer

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

Question 4

Find the instantaneous rate of change for the function at the value given.
-Find the instantaneous rate of change for the function x2 + 6x at x = 3.

Accepted Answer

A) 27 
B) 9 
C) 6 
D) 12 
A) 27 
B) 9 
C) 6 
D) 12

Question 5

Provide an appropriate response.
-Find

Accepted Answer

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

Question 6

Solve the problem.
-If an object moves along a line so that it is at   at time x (in seconds), find the instantaneous velocity function v = f'(x).

Accepted Answer

A)    
B)  6x+7 
C)    
D)  3x+7 
A)    
B)  6x+7 
C)    
D)  3x+7

Question 7

Provide an appropriate response.
-The total cost in dollars of producing x lawn mowers is given by C(x) =   Find the marginal
average cost at x = 20,   and interpret the result.

Accepted Answer

A)  -$10.33; a unit increase in production will decrease the average cost per unit by approximately $10.33 ata
production level of 20 units. 
B)  -$13.33; a unit increase in production will decrease the average cost per unit by approximately $13.33 ata
production level of 20 units. 
C) -$1.33; a unit increase in production will decrease the average cost per unit by approximately $1.33 at a
production level of 20 units. 
D)  -$20.33; a unit increase in production will decrease the average cost per unit by approximately $20.33 at a
production level of 20 units. 
A)  -$10.33; a unit increase in production will decrease the average cost per unit by approximately $10.33 ata
production level of 20 units. 
B)  -$13.33; a unit increase in production will decrease the average cost per unit by approximately $13.33 ata
production level of 20 units. 
C) -$1.33; a unit increase in production will decrease the average cost per unit by approximately $1.33 at a
production level of 20 units. 
D)  -$20.33; a unit increase in production will decrease the average cost per unit by approximately $20.33 at a
production level of 20 units.

Question 8

Sketch a possible graph of a function that satisfies the given conditions.
-f(-1) = -7 ;

Accepted Answer

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

Question 9

Solve the problem.
-Suppose the demand for a certain item is given by   where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

Accepted Answer

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

Question 10

Solve the problem.
-A company is planning to manufacture a new blender.After conducting extensive market surveys,the research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly demand of 800 blenders at a price of $40 per blender.Assuming the demand equation is linear,use the research department's estimates to find the revenue equation in terms of the demand x.

Accepted Answer

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

Question 11

List the x-values in the graph at which the function is not differentiable.
-

Accepted Answer

A) x = 2 
B) x = -2,x = 2 
C) x = 0 
D) x = -2,x = 0,x = 2 
A) x = 2 
B) x = -2,x = 2 
C) x = 0 
D) x = -2,x = 0,x = 2

Question 12

Solve the problem.
-The demand equation for a certain item is   and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result.

Accepted Answer

A) $14; at the 3,000 level of production,profit will increase by approximately $14 for each unit increase in production. 
B) $16; at the 3,000 level of production,profit will increase by approximately $16 for each unit increase in production. 
C) $7; at the 3,000 level of production,profit will increase by approximately $7 for each unit increase in production. 
D) $4; at the 3,000 level of production,profit will increase by approximately $4 for each unit increase in production. 
A) $14; at the 3,000 level of production,profit will increase by approximately $14 for each unit increase in production. 
B) $16; at the 3,000 level of production,profit will increase by approximately $16 for each unit increase in production. 
C) $7; at the 3,000 level of production,profit will increase by approximately $7 for each unit increase in production. 
D) $4; at the 3,000 level of production,profit will increase by approximately $4 for each unit increase in production.

Question 13

Provide an appropriate response.
-y = x4 + 2x3 + 2x + 2 at x = -3

Accepted Answer

A) 65 
B) -52 
C) 67 
D) -50 
A) 65 
B) -52 
C) 67 
D) -50

Question 14

Find average rate of change for the function over the given interval.
-Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y = x2 + 3x.

Accepted Answer

A) 22 
B) 4 
C) 9 
D) 11 
A) 22 
B) 4 
C) 9 
D) 11

Question 15

Find dy.
-Find dy.
y=

Accepted Answer

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

Question 16

Provide an appropriate response.
-Use a graphing utility to find the discontinuites of the given rational function.

Accepted Answer

A)  -1 
B)  3 
C)  1 
D)  Continious at all values of x 
A)  -1 
B)  3 
C)  1 
D)  Continious at all values of x

Question 17

Provide an appropriate response.
-

Accepted Answer

A) y = 216x + 54 
B) y = 54x + 216 
C) y = 18x + 216 
D) y = 216x + 18 
A) y = 216x + 54 
B) y = 54x + 216 
C) y = 18x + 216 
D) y = 216x + 18

Question 18

Suppose an object moves along the y-axis so that its location is y =   at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

Accepted Answer

A)  8 m/s 
B)  9 m/s 
C)  20 m/s 
D)  10 m/s 
A)  8 m/s 
B)  9 m/s 
C)  20 m/s 
D)  10 m/s

Use the definition f'(x) = to find the derivative at x. -f(x) = 10 - 3x²

Provide an appropriate response. -Find f'(x) if f(x) =π.

Provide an appropriate response. -Find the values of x where the tangent line is horizontal for f(x) = 3x³ - 2x² - 9.

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function x² + 6x at x = 3.

Provide an appropriate response. -Find

Solve the problem. -If an object moves along a line so that it is at at time x (in seconds), find the instantaneous velocity function v = f'(x).

Provide an appropriate response. -The total cost in dollars of producing x lawn mowers is given by C(x) = Find the marginal average cost at x = 20, and interpret the result.

Sketch a possible graph of a function that satisfies the given conditions. -f(-1) = -7 ;

Solve the problem. -Suppose the demand for a certain item is given by where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

List the x-values in the graph at which the function is not differentiable. -

Solve the problem. -The demand equation for a certain item is and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result.

Provide an appropriate response. -y = x⁴ + 2x³ + 2x + 2 at x = -3

Find average rate of change for the function over the given interval. -Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y = x² + 3x.

Find dy. -Find dy. y=

Provide an appropriate response. -Use a graphing utility to find the discontinuites of the given rational function.

Provide an appropriate response. -

Suppose an object moves along the y-axis so that its location is y = at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

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Exam 9: Markov Chains

Use the definition f'(x) = to find the derivative at x. -f(x) = 10 - 3x2

Provide an appropriate response. -Find f'(x) if f(x) =π.

Provide an appropriate response. -Find the values of x where the tangent line is horizontal for f(x) = 3x3 - 2x2 - 9.

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function x2 + 6x at x = 3.

Provide an appropriate response. -Find

Solve the problem. -If an object moves along a line so that it is at at time x (in seconds), find the instantaneous velocity function v = f'(x).

Provide an appropriate response. -The total cost in dollars of producing x lawn mowers is given by C(x) = Find the marginal average cost at x = 20, and interpret the result.

Sketch a possible graph of a function that satisfies the given conditions. -f(-1) = -7 ;

Solve the problem. -Suppose the demand for a certain item is given by where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

List the x-values in the graph at which the function is not differentiable. -

Solve the problem. -The demand equation for a certain item is and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result.

Provide an appropriate response. -y = x4 + 2x3 + 2x + 2 at x = -3

Find average rate of change for the function over the given interval. -Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y = x2 + 3x.

Find dy. -Find dy. y=

Provide an appropriate response. -Use a graphing utility to find the discontinuites of the given rational function.

Provide an appropriate response. -

Suppose an object moves along the y-axis so that its location is y = at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

Linear Equations and Graphs

Mathematics of Finance

Linear Inequalities and Linear Programming

Logic, sets, and Counting

Probability

Limits and the Derivative

Mathematical Functions and Limits

Filters

Use the definition f'(x) = to find the derivative at x. -f(x) = 10 - 3x²

Provide an appropriate response. -Find the values of x where the tangent line is horizontal for f(x) = 3x³ - 2x² - 9.

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function x² + 6x at x = 3.

Provide an appropriate response. -y = x⁴ + 2x³ + 2x + 2 at x = -3

Find average rate of change for the function over the given interval. -Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y = x² + 3x.