Let . Which statement correctly characterizes as…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let h(x)=(x−1)1/3+2h(x)=(x-1)^{1/3}+2. Which statement correctly characterizes h′(x)h'(x) as x→1x\to 1? (a) h′(x)→0h'(x)\to 0, so the tangent line is horizontal at x=1x=1. (b) h′(x)h'(x) approaches a finite non-zero constant equal to 13\tfrac13. (c) h′(x)h'(x) grows without bound, indicating a vertical tangent at x=1x=1. (d) h′(x)→−∞h'(x)\to -\infty, showing a vertical tangent slanted downward at x=1x=1.

Related theory

Browse the problem library