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Let f(x)=|cosx-sinx|, then f'((pi)/(4)) ...

Let `f(x)=|cosx-sinx|,` then `f'((pi)/(4))` is equal to

A

`sqrt(2)`

B

`-sqrt(2)`

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`f(x)=|cosx-sinx|`
`implies" "f(x)={{:(cosx-sinx","," for "0ltxle(pi)/(x)),(sinx-cosx","," for "(pi)/(4)ltxlt(pi)/(2)):}`
Clearly,
(LHD at `x=pi//4`)`={(d)/(dx)(cosx-sinx)}_("at"x=pi//4)`
`=(-sinx-cosx)_(x=pi//4)=-sqrt(2)`
and,
(RHD at `x=pi//4`)`={(d)/(dx)(sinx-cosx)}_("at"x=pi//4)`
`=(cosx+sinx)_(x=pi//4)=sqrt(2)`
`:." "("LHD at "x=pi//4)ne("RHD at "x=pi//4)`
Thus, `f'(pi//4)` does not exist.
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Section I - Solved Mcqs
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