Exam 3: Section 3: Differentiation

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Suppose that an automobile's velocity starting from rest is Suppose that an automobile's velocity starting from rest is   where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place. where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.

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B

When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle   shown in the figure. Let h represent the satellite's distance from Earth's surface and let r represent Earth's radius. Find the rate at which h is changing with respect to   when   (Assume r = 4460 miles.) Round your answer to the nearest unit.  shown in the figure. Let h represent the satellite's distance from Earth's surface and let r represent Earth's radius. Find the rate at which h is changing with respect to When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle   shown in the figure. Let h represent the satellite's distance from Earth's surface and let r represent Earth's radius. Find the rate at which h is changing with respect to   when   (Assume r = 4460 miles.) Round your answer to the nearest unit.  when When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle   shown in the figure. Let h represent the satellite's distance from Earth's surface and let r represent Earth's radius. Find the rate at which h is changing with respect to   when   (Assume r = 4460 miles.) Round your answer to the nearest unit.  (Assume r = 4460 miles.) Round your answer to the nearest unit. When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle   shown in the figure. Let h represent the satellite's distance from Earth's surface and let r represent Earth's radius. Find the rate at which h is changing with respect to   when   (Assume r = 4460 miles.) Round your answer to the nearest unit.

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A

The length of a rectangle is The length of a rectangle is   and its height is   , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time. and its height is The length of a rectangle is   and its height is   , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time. , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.

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D

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

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Find the second derivative of the function Find the second derivative of the function   . .

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Find the derivative of the algebraic function Find the derivative of the algebraic function   . .

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Find the second derivative of the function Find the second derivative of the function   . .

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

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Use the Quotient Rule to differentiate the function Use the Quotient Rule to differentiate the function   . .

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Find the second derivative of the function Find the second derivative of the function   . .

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Use the quotient rule to differentiate the following function Use the quotient rule to differentiate the following function   and evaluate   . and evaluate Use the quotient rule to differentiate the following function   and evaluate   . .

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A population of 620 bacteria is introduced into a culture and grows in number according to the equation A population of 620 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 t = 2. Round your answer to two decimal places. where t is measured in hours. Find the rate at which the population is growing when t = 2. Round your answer to two decimal places.

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The ordering and transportation cost C for the components used in manufacturing a product is 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 x = 24. Round your answer to two decimal places. 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 x = 24. Round your answer to two decimal places.

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The radius of a right circular cylinder is The radius of a right circular cylinder is   and its height is   , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time. and its height is The radius of a right circular cylinder is   and its height is   , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time. , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time.

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Find the derivative of the function Find the derivative of the function   . .

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

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Find the derivative of the function Find the derivative of the function   . .

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Use the Product Rule to differentiate Use the Product Rule to differentiate   . .

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Use the Quotient Rule to differentiate the function Use the Quotient Rule to differentiate the function   . .

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Use the Quotient Rule to differentiate the function Use the Quotient Rule to differentiate the function   . .

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