Question

For $xϵ(0,\frac{5\pi }{2}),definef\left(x\right)={\int }_0^x\sqrt{t}sintdt.$ Then f has

• A. local minimum at $\pi$ and 2 $\pi$
• B. local minimum at $\pi$ and local maximum at 2$\pi$
• C. local maximum at $\pi$ and local minimum at 2$\pi$
• D. local maximum at $\pi$ and 2$\pi$

Answer 1

The correct option is C local maximum at $\pi$ and local minimum at 2$\pi$

$f^{\prime }\left(x\right)=\sqrt{x}sinx$
$Givenxϵ(0,\frac{5\pi }{2})$
f ' (x) changes sign from +ve to – ve at $\pi$
f ' (x) changes sign from - ve to + ve at 2 $\pi$
f' has local max at $\pi$, local min at 2 $\pi$