Consider the function f(x)= cases x^ 2 , & x 0

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

Problem

Consider the function f(x)={x2,x≤0,x,x>0.f(x)=\begin{cases} x^{2}, & x\le 0,\\ \sqrt{x}, & x>0. \end{cases} Identify the point(s) at which ff fails to be differentiable and state whether the failure corresponds to a corner, a cusp, or a vertical tangent.

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