For the composite function y = f(g(x))

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For the composite function y = f(g(x)), suppose that at x = 4 the following are true: • g′(4)<0g'(4) < 0 • f′(g(4))<0f'(g(4)) < 0 Which statement best describes the behavior of y near x = 4? (a) yy is decreasing because dydx<0\dfrac{dy}{dx}<0 (b) yy is increasing because dydx>0\dfrac{dy}{dx}>0 (c) yy has a horizontal tangent because dydx=0\dfrac{dy}{dx}=0 (d) The behavior cannot be determined without knowing the magnitudes of g′(4)g'(4) and f′(g(4))f'(g(4))

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