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

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