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AP Calculus AB :: 2006-2007 :: Shubleka
Name______________________________ Page 1
Quiz Six: Applications of the Derivative Problem One (10 points) Suppose that f and g are both concave upward on , . Under what condition(s) will the composite function h f g be concave upward ? Problem Two (10 points) Find a cubic function f ( x) ax 3 bx 2 cx d that has a local maximum value of 3 at -2 and a local minimum value of 0 at 1. Problem Three (10 points) Let K (t ) be a measure of the knowledge you will gain by studying for the AP Calculus final exam for t hours. Which do you think is larger, K (8) K (7) or K (4) K (3) ? Is the graph of K concave upward or concave downward? Justify your reasoning. Problem Four (10 points) Sketch the graph of a function that satisfies all of the following:
f '(2) 0,
f (2) 1,
f (0) 0,
f '( x) 0 if 0 x 2, f '( x) 0 if f ''( x) 0 if 0 x 1 or if x 4 f ''( x) 0 if 1 x 4, lim f ( x) 1 x
f ( x) f (x) x R.
x 2
Name______________________________ Page 1
Quiz Six: Applications of the Derivative Problem One (10 points) Suppose that f and g are both concave upward on , . Under what condition(s) will the composite function h f g be concave upward ? Problem Two (10 points) Find a cubic function f ( x) ax 3 bx 2 cx d that has a local maximum value of 3 at -2 and a local minimum value of 0 at 1. Problem Three (10 points) Let K (t ) be a measure of the knowledge you will gain by studying for the AP Calculus final exam for t hours. Which do you think is larger, K (8) K (7) or K (4) K (3) ? Is the graph of K concave upward or concave downward? Justify your reasoning. Problem Four (10 points) Sketch the graph of a function that satisfies all of the following:
f '(2) 0,
f (2) 1,
f (0) 0,
f '( x) 0 if 0 x 2, f '( x) 0 if f ''( x) 0 if 0 x 1 or if x 4 f ''( x) 0 if 1 x 4, lim f ( x) 1 x
f ( x) f (x) x R.
x 2
