FinalFR2008

Calculus: Early Transcendental Functions

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Free Response Final 2008 Name 1. The graph of a differentiable function, f H t L , on the closed interval @ - 2, 10 D is shown below. The graph of f H t L has horizontal tangent lines at x = 0, x = 4, and x = 8. The function g H x L is defined by g H x L = 3 + 4 x f H t L dt on the interval @ - 2, 10 D - 2 - 1 1 2 3 4 5 6 7 8 9 10 - 2 - 1 1 2 3 4 f H t L H A L Find g H 4 L , g ¢ H 4 L , and g ¢ ¢ H 4 L H B L On what intervals is g H x L increasing? Justify your answer. H C L On what intervals is g H x L concave up? Justify your answer. H D L Find a trapezoidal approximation for - 2 10 f H t L dt using 6 subintervals of length D t = 2. 2. A cup has the shape of a right circular cone, as shown below. The height of the cup is 12 inches, and the radius of the top is 6 inches. Water in the cup is evaporating at the rate of - 1 ÄÄÄÄÄÄÄÄ 3 inches 3 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄ minute . The volume of the cone is V = p ÄÄÄÄ 3 r 2 h 12 6 h r
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H A L Find the volume of the water in the cup when h = 4 inches. Indicate units of measure.
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