Sketch the graph of a continuous function $y=h(x)…

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Problem 67

Sketch the graph of a continuous function $y=g(x)$ such that $$\begin{array}{c}{\text { a. } g(2)=2,0 < g^{\prime}<1 \text { for } x < 2, g^{\prime}(x) \rightarrow 1^{-} \text { as } x \rightarrow 2^{-}} \\ {-1< g^{\prime} < 0 \text { for } x > 2, \text { and } g^{\prime}(x) \rightarrow-1^{+} \text { as } x \rightarrow 2^{+}}\end{array}$$ $$\begin{array}{l}{\text { b. } g(2)=2, g^{\prime}<0 \text { for } x<2, g^{\prime}(x) \rightarrow-\infty \text { as } x \rightarrow 2^{-}} \\ {g^{\prime}>0 \text { for } x>2, \text { and } g^{\prime}(x) \rightarrow \infty \text { as } x \rightarrow 2^{+} \text { . }}\end{array}$$

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