If and are differentiable functions for such that , , ,

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

Problem

f(x)

and

g(x)

are differentiable functions for

0 \leq x \leq 1

such that

f(0) = 10

g(0) = 2

f(1) = 2

g(1) = 4

, then in the interval

(0, 1)

(a)

f'(x) = 0

for all

x

(b)

f'(x) + 4g'(x) = 0

for at least one

x

(c)

f'(x) = 2g'(x)

for at most one

x

(d) none of these