Let f(x)= cases x^2, & x 1, 2x-1, & x>1

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let f(x)={x2,x≤1,2x−1,x>1.f(x)=\begin{cases} x^2, & x\le 1,\\ 2x-1, & x>1. \end{cases} Determine whether ff is differentiable at x=1x=1. If it is, state the value of f′(1)f'(1); if it is not, state that the derivative does not exist.

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