Question

Which of the following is not a decreasing function on the interval $\left( 0,\frac{\pi}{2} \right)$

• A. $\cos x$
• B. $\cos 2x$
• C. $\cos 3x$
• D. $\cot x$

Answer 1

Answer: (C)

$\cos 3x$

Answer 2

Obviously, here $\cos 3x$ in not decreasing in $\left( 0,\frac{\pi}{2} \right)$ because $\frac{d}{dx}\cos 3x = - 3\sin 3x$.

But at $x = 75^{o}$, $- 3\sin 3x > 0$. Hence the result.