FinalFR2005

Calculus: Early Transcendental Functions

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Free Response Final 2005 1. Consider the function f H x L = 2 x cccccccccccccccc x 2 + 4 H A L Find f ± H x L and the critical points from this derivative H B L Find f ±± H x L and the critical points from this second derivative H C L Use H A L and H B L above to sketch the curve of f H x L = 2 x ccccccccccccccc x 2 + 4 5 4 3 2 1 1 2 3 4 5 x 1 0.75 0.5 0.25 0.25 0.5 0.75 1 y
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2. A circle is inscribed in a square, as shown below. The circumference of the circle is increasing at a constant rate of 6 inches per second. As the circle expands, the square expands to maintain the condition of tangency. H A L Find the rate at which the perimeter of the square is increasing. Indicate units of measure. H B L At the instant where the area of the circle is 25 π inches 2 , find rate of increase in the area enclosed between the circle and the square. Indicate units of measure.
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3. The rate of consumption of cola in the United States is given by S H t L = Ce kt , where S is measured
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This document was uploaded on 10/16/2011.

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FinalFR2005 - Free Response Final 2005 1. Consider the...

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