At x = 2, the graph of u = g(x) has a horizontal tangent so that g'(2) = 0. Assume…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
At x = 2, the graph of u = g(x) has a horizontal tangent so that g'(2) = 0. Assume that the derivative f'(u) exists and is non-zero at u = g(2). What is the value of dxdy at x = 2 for the composite function y = f(g(x))?
(a) Undefined because g′(2)=0
(b) f′(g(2))
(c) 0
(d) Positive but not zero