Exam 4: Applications of Differentiation

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What is the minimum vertical distance between the parabolas What is the minimum vertical distance between the parabolas   and   ? and What is the minimum vertical distance between the parabolas   and   ? ?

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Determine where the graph of the function Determine where the graph of the function   is concave upward and where it is concave downward. Also, find all inflection points of the function. is concave upward and where it is concave downward. Also, find all inflection points of the function.

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Find the point on the line Find the point on the line   that is closest to the origin. that is closest to the origin.

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What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in   s? s?

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Use the Second Derivative Test to find the relative extrema, if any, of the function Use the Second Derivative Test to find the relative extrema, if any, of the function   . .

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A particle is moving with the given data. Find the position of the particle. A particle is moving with the given data. Find the position of the particle.   ,  , A particle is moving with the given data. Find the position of the particle.   ,

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The graph of the first derivative The graph of the first derivative   of a function f is shown below. At what values of x does f have a local maximum or minimum?  of a function f is shown below. At what values of x does f have a local maximum or minimum? The graph of the first derivative   of a function f is shown below. At what values of x does f have a local maximum or minimum?

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Find f. Find f.

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