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The maximum and minimum values of f(x)= ...

The maximum and minimum values of `f(x)= 6 sin x cos x +4cos2x` are respectively

A

`5 and -5`

B

`2sqrt13 and -2 sqrt13`

C

`10 and -10`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `6 sinx cos x+4cos2x=3sin2x+4cos2x`
Now, `-sqrt(3^(2)-4^(2))le3 sin 2x+4 cos 2x lesqrt(3^(2)+4^(2))"for all" x implies-5le6sinx x cosx+4cos2x le5"for all x"`
Hence, the maximum and minimum values of
`3 sin2x+4cos2xare5and -5` respectively.
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