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Maximum value of f(x)=sinx+cosx is :...

Maximum value of `f(x)=sinx+cosx ` is `:`

A

1

B

2

C

`(1)/(sqrt(2))`

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`y=f(x)=sinx+cosx`
`(dy)/(dx)=cosx-sinx`
`(dy)/(dx)=0,sinx=cosx,tanx=1`
`x=45^(@)`
`y=sin45^(@)+cos45^(@)`
`=(1)/(sqrt(2))+(1)/sqrt(2)`
`=(2)/(sqrt(2))=sqrt(2)`
Alter `:fx=sqrt(2)sin(x+(pi)/(4))`
`f(x)_(max)=sqrt(2)`
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