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Let f: R to R and g:R to R be respectiv...

Let f:` R to R and g:R to R` be respectively given by `f(x) =|x|+1 and g(x) =x^(2)+1)`. Define `h: R to R ` by
`h(x) ={{:( max{f(x) , g(x) },if xle0),(min{f(x) ,g(x) },if x gt 0):}`
then number of point at which h(x) is not differentiable is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, `h(x)={{:(,x^(2)+1,(-oo","-1)),(,-x+1,[-1","0]),(,x^(2)+1,x in[0","1]),(,x+1,x in [1","oo)):}`
It is evident from the graph of h(x) that it is not differentiable at (-1,2),(0,1) and (1,2)
It is evident from the graph of h(x) that it is not differentiable at (-1,2), (0,1) and (1,2).
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