The function x - x is increasing in the interval - Vidyadip

MCQ

The function $\sin x - \cos x$ is increasing in the interval

A
$\left[ {{{3\pi } \over 4},{{7\pi } \over 4}} \right]$
✓
$\left[ {0,{{3\pi } \over 4}} \right)$
C
$\left[ {{\pi \over 4},{{3\pi } \over 4}} \right]$
D
None of these

✓

Answer

Correct option: B.

$\left[ {0,{{3\pi } \over 4}} \right)$

b
(b) We have, $f'(x) = \cos x + \sin x$

Now $f(x)$ is increasing function of $x$ , if

$f'(x) = \cos x + \sin x > 0$ or $\sqrt 2 \cos \left( {x - \frac{\pi }{4}} \right) > 0$

==>$0 \le x < \frac{{3\pi }}{4}i.e.\,\,\,f'(x) > 0$ in $\left[ {0,\frac{{3\pi }}{4}} \right)$.

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