Let f(x)=(sinx)/x and g(x)=|x.f(x)|+||x-...

Let `f(x)=(sinx)/x` and g(x)=|x.f(x)|+||x-2|-1|. Then, in the interval `(0,3pi)` g(x) is :

A

not differentiable at 2 points

B

not differentiable at 4 points

C

not differentiable at 5 points

D

None of these

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The correct Answer is:

C

Here, `f(x)=(sin x)/x` So, `g(x)=|x.(sinx)/x|+||x-2|-1|=|sin x|+||x-2|-1|`

Clearly, from the graphs, g(x) is not differentiable at `pi,2pi`,1,2,3 in `(0,3pi)`
Hence, g(x) is not differentiable at 5 points.

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