Let f(x)= cases 2x+1,& x<3 x^ 2 -5,& x 3 cases Determine whether exists

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

Problem

Let f(x)={2x+1,x<3x2−5,x≥3f(x)=\begin{cases}2x+1,& x<3\\ x^{2}-5,& x\ge 3\end{cases} Determine whether f′(3)f'(3) exists. State the value if it exists, or indicate that it does not exist.

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