Sketch the graph of a differentiable function $y=…

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Problem 65

Sketch the graph of a differentiable function $y=f(x)$ through the point $(1,1)$ if $f^{\prime}(1)=0$ and $$ \begin{array}{l}{\text { a. } f^{\prime}(x)>0 \text { for } x<1 \text { and } f^{\prime}(x)<0 \text { for } x>1} \\ {\text { b. } f^{\prime}(x)<0 \text { for } x<1 \text { and } f^{\prime}(x)>0 \text { for } x>1} \\ {\text { c. } f^{\prime}(x)>0 \text { for } x \neq 1} \\ {\text { d. } f^{\prime}(x)<0 \text { for } x \neq 1}\end{array} $$

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