Let for , and for . The value of with at which…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f(t) = t^2

for

0 \leq t \leq 1

, and

g(t) = t^3

for

0 \leq t \leq 1

. The value of

c

with

0 < c < 1

at which

\frac{f(1) - f(0)}{g(1) - g(0)} = \frac{f'(c)}{g'(c)}

is (a)

\frac{2}{3}

(b)

\frac{1}{3}

(c)

\frac{1}{2}

(d)

\frac{1}{6}

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