The function f(x) = x - 2px is monotonically decreasing for - Vidyadip

MCQ

The function $f(x) = \cos x - 2px$ is monotonically decreasing for

A
$p < {1 \over 2}$
✓
$p > {1 \over 2}$
C
$p < 2$
D
$p > 2$

✓

Answer

Correct option: B.

$p > {1 \over 2}$

b
(b) $f(x)$ will be monotonically decreasing, if $f'(x) < 0$.

==> $f'(x) = - \sin x - 2p < 0$ ==>$\frac{1}{2}\sin x + p > 0$

==> $p>\frac{1}{2}\,,\,\,[\because -1\le \sin x\le 1]$

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