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Let f(x)=(x^(2)-3x+2)(x^(3)-6x^(2)+11x...

Let
`f(x)=(x^(2)-3x+2)(x^(3)-6x^(2)+11x-6)|+|sin(x+(pi)/(4))|` The set of points at which the function f(x) is not differentiable in `[0,2pi]` is

A

`{1,2,3,(3pi)/(4),(7pi)/(4)}`

B

`{1,2,3}`

C

`{3,(3pi)/(4),(7pi)/(4)}`

D

`{(pi)/(4),(3pi)/(4),(5pi)/(4)}`

Text Solution

Verified by Experts

The correct Answer is:
3
`f(x)=(x-1)(x-2)|(x-1)(x-2)(x-3)|+|sin (x+pi//4)|`
Where (x-1)(x-2)(x-3) is not differentiable at x=3 `sin(X+pi//4))` is not differentiable at `x+(pi)/(4)=pi,2pi`
`implies x=(3pi)/(4),(7pi)/(4)`
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