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Exam 2: The Derivative

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Question 81

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Answer true or false. If , .

A) True
B) False

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Question 82

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Find , if .

A) 30x⁵
B) 6x⁵ - 6
C)
D) 5x⁵
E)

F) A) and C)
G) C) and E)

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Question 83

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Let f(x) = 3x². Find the slope of the tangent to the graph of f at a general point x₀ using limits and find the slope of the tangent at x₀ = 3.

Find dy/dx if y = 5x⁸.

Find f '(x) if f(x) = x sin x.

Find the instantaneous rate of change of y = 3x² with respect to x at x₀ = 5.

Answer true or false. If , .

The cost of manufacturing an object is given by C = f(x) dollars. Estimate the cost of making the 310^th item if f '(309) = $74.

Let . Use the definition of the derivative to find .

Let f(x) = sin x. Estimate by using a graphing utility.

Use the definition of the derivative to calculate f '(x) if f(x) = 4x⁴ + 7 and find the equations of the tangent line and the normal line to the graph of f at x = -4.

Use the definition of the derivative to calculate f '(x) if f(x) = 2x² - 2x and find the equation of the tangent line and the normal line to the graph of f at x = 2.

Answer true or false. The derivative of the function graphed on the left is graphed on the right.

f(x) = sin(6x) . f'(x) =

Find the equation of the tangent line to at x = 8.

Let . Find the instantaneous rate of change of y with respect to x at the point x = 5.

Answer true or false. If x is given in radians, the derivative formula for y = sin x in degrees is .

Find where f(x) = sin ⁶ 5x.

Find equations for the tangent and normal lines to the graph of f(x) = cos(4 - x²) at x = 2.

Find f '(x) if f(x) = x tan x.