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f(x)=sin+sqrt(3)cosx is maximum when x= ...

`f(x)=sin+sqrt(3)cosx` is maximum when `x=` `pi/3` (b) `pi/4` (c) `pi/6` (d) 0

A

`60^(@)`

B

`30^(@)`

C

`45^(@)`

D

`0^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `f(x)=sin x +sqrt(3) cos x`s
`f'(x)=cosx=sqrt(3)sinx` and
`f"(x)=-sinx-sqrt(3)cosx`
For maximum, put `f'(x)=0`
therefore `x^(2)-32x+240=0`
i.e. `(x-12)(x-20)=0`
`:.x=12` or `x!=20`
`:.20-x=20-12=8`
Now `f"(x)=20x^(3)-480x^(2)+2400x`
`impliesf''(12)=345600-69120+28800=-5760lt0`
Here `f` is maximum at `x=12`.
Hence 12 and 8 are two part of 20.
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