Limit Continuity And Differentiability Ques 60
- 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)=\left\{\begin{array}{cl} \max \{f(x), g(x)\}, & \text { if } x \leq 0 . \\ \min \{f(x), g(x)\}, & \text { if } x>0 . \end{array}\right. $
The number of points at which $h(x)$ is not differentiable is
(2014 Adv.)
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Answer:
Correct Answer: 60.$(3)$
Solution: PLAN
(i) In these type of questions, we draw the graph of the function.
(ii) The points at which the curve taken a sharp turn, are the points of non-differentiability.
Curve of $f(x)$ and $g(x)$ are
$h(x)$ is not differentiable at $x= \pm 1$ and 0 .
As, $h(x)$ take sharp turns at $x= \pm 1$ and 0 .
Hence, number of points of non-differentiability of $h(x)$ is 3 .
BETA
