Question 54

Let $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be respectively given by $$f(x) = |x| + 1$$ and $$g(x) = x^2 + 1$$. Define $$h:R \rightarrow R$$ by $$h(x) = \begin{cases}max \left\{f(x), g(x)\right\} & if x \leq 0,\\min \left\{f(x), g(x)\right\} & if x > 0\end{cases}$$
The number of points at which h(x) is not differentiable is

Correct Answer: 3

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