Define h(x)=|x-2|+(x-2)^2

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Define h(x)=∣x−2∣+(x−2)2.h(x)=|x-2|+(x-2)^2. The graph of hh appears smooth except possibly at x=2x=2. (1) Part (a) — Algebraic preparation of the difference quotient (2) Part (b) — One-sided limit evaluations (3) Part (c) — Decision on differentiability at x=2x=2 (4) Part (d) — Full differentiability profile of hh

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