Exam 3: Section 4 : Differentiation

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

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C

Find Find   if   . if Find   if   . .

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E

If the annual rate of inflation averages If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. over the next If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. years, the approximate cost If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. of goods or services during any year in that decade is If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. where If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. is the time in years and If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. is the present cost. The price of an oil change for your car is presently If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. . Estimate the price If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Estimate the price   years from now. Round your answer to two decimal places. years from now. Round your answer to two decimal places.

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B

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

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

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

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

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A buoy oscillates in simple harmonic motion A buoy oscillates in simple harmonic motion   as waves move past it. The buoy moves a total of 3.5 feet (vertically) between its low point and its high point. It returns to its high point every 14 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0. as waves move past it. The buoy moves a total of 3.5 feet (vertically) between its low point and its high point. It returns to its high point every 14 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0.

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

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A buoy oscillates in simple harmonic motion A buoy oscillates in simple harmonic motion   as waves move past it. The buoy moves a total of 13.5 feet (vertically) between its low point and its high point. It returns to its high point every 10 seconds. Determine the velocity of the buoy as a function of t. as waves move past it. The buoy moves a total of 13.5 feet (vertically) between its low point and its high point. It returns to its high point every 10 seconds. Determine the velocity of the buoy as a function of t.

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

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

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Find Find   if   . if Find   if   . .

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

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

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If the annual rate of inflation averages If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. over the next If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. years, the approximate cost If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. of goods or services during any year in that decade is If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. where If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. is the time in years and If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. is the present cost. The price of an oil change for your car is presently If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. . Find the rate of change of If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. with respect to If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. when If the annual rate of inflation averages   over the next   years, the approximate cost   of goods or services during any year in that decade is   where   is the time in years and   is the present cost. The price of an oil change for your car is presently   . Find the rate of change of   with respect to   when   . Round your answer to three decimal places. . Round your answer to three decimal places.

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Find Find   if   . if Find   if   . .

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

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

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