Mathematics

Problem

For the composite function y = f(g(x)), suppose that at x = 4 the following are true: •

g'(4) < 0

•

f'(g(4)) < 0

Which statement best describes the behavior of y near x = 4? a)

y

is decreasing because

\dfrac{dy}{dx}<0

y

is increasing because

\dfrac{dy}{dx}>0

y

has a horizontal tangent because

\dfrac{dy}{dx}=0

d) The behavior cannot be determined without knowing the magnitudes of

g'(4)

and

f'(g(4))