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The interval in which the function f(x)=...

The interval in which the function f(x)=sin x-cos x -ax +b decreases for all real values of x is given by

A

`agesqrt2`

B

`age1`

C

`altsqrt2`

D

`alt1`

Text Solution

Verified by Experts

The correct Answer is:
1
Since f(x) decreases for all x, therefore
`f'(x)le0forallx`
`rArrcos x +sin x-ale0forallx`
`rArrsinx+cosxleaforallx`
`rArrsin(x+(pi)/(4))le(a)/sqrt2forallx`
`rArr(a)/(sqrt2)ge1[becausesin(x+(pi)/(4))le1]`
`rArragesqrt2`
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