Question

Number of critical points of the function, $f(x)=\frac{2}{3} \sqrt{x^3}-\frac{x}{2}+\int\limits_1^x\left(\frac{1}{2}+\frac{1}{2} \cos 2 t-\sqrt{t}\right) d t$ which lie in the interval $[-2 \pi, 2 \pi]$ is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (B)

note that $f$ is defined for $x >0$
$f ^{\prime}( x )=\frac{1}{2} \cos 2 x =0 \Rightarrow x = n \pi \pm \frac{\pi}{4} \Rightarrow$