Consider the function f(x)= cases x^ 2 , & x 1, 2x-1, & x>1

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

Problem

Consider the function f(x)={x2,x≤1,2x−1,x>1.f(x)=\begin{cases} x^{2}, & x\le 1,\\ 2x-1, & x>1. \end{cases} (1) Part 1: Part (a) — Continuity analysis at x=1x=1 (2) Part 2: Part (b) — Left-hand and right-hand difference quotients (3) Part 3: Part (c) — Conclusion on differentiability with justification

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