Browse Questions

# At what point in the interval $[0,2\pi]$ does the function $\sin2x$ attain its maximum value?

Toolbox:
• At maxima $f\: ' (x) = 0$
Step 1

$2cos\: 2x = 0\: \Rightarrow x = \large\frac{\pi}{4}, \: \large\frac{3\pi}{4},\: \large\frac{5\pi}{4},\: \large\frac{7\pi}{4}$
Step 2
$f \:" (x) = -4sin\: 2x$ is negative when $x = \large\frac{\pi}{4}, \: \large\frac{5\pi}{4}$
Ans : At $x = \large\frac{\pi}{4}\: and \: \large\frac{5\pi}{4}\: f(x)$ attains maximum value.