Problem 97E

97. Let

$$f(x)=\left\{\begin{array}{ll}x^{2}+1 & \text { if } x<1 \\x+1 & \text { if } x>1\end{array}\right.$$

Is $f$ differentiable at 1 ? Sketch the graphs of $f$ and $f^{\prime}$.

 

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