The function f(x) = cos x - 2px is monotonica | vedclass

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(B) function $f(x)$ is monotonically decreasing if its derivative $f'(x) \le 0$ for all $x$ in the domain.Given $f(x) = \cos x - 2px$.First,find the d

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$p > \frac{1}{2}$

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(B) function $f(x)$ is monotonically decreasing if its derivative $f'(x) \le 0$ for all $x$ in the domain.Given $f(x) = \cos x - 2px$.First,find the derivative: $f'(x) = -\sin x - 2p$.For $f(x)$ to be monotonically decreasing,we require $f'(x) \le 0$.$-\sin x - 2p \le 0$$\sin x + 2p \ge 0$$2p \ge -\sin x$$p \ge -\frac{1}{2} \sin x$.Since the maximum value of $-\frac{1}{2} \sin x$ is $\frac{1}{2}$ (when $\sin x = -1$),for the inequality to hold for all $x$,we must have $p \ge \frac{1}{2}$.Thus,the function is monotonically decreasing for $p \ge \frac{1}{2}$.

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

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