Q116 / 170 · Manipal (MET) 2017 · Mathematics
The function $y=a(1-\cos x)$ is maximum when $x$ is equal to
- Correct answerA$\pi$
- B$\frac{\pi}{2}$
- C$-\frac{\pi}{2}$
- D$-\frac{\pi}{6}$
Solution
Given, $y=a(1-\cos x)$
On differentiating w.r.t. $x$, we get
$\frac{d y}{d x}=a \sin x$
Again differentiating w.r.t. $x$, we get
$\frac{d^2 y}{d x^2}=a \cos x$
Put $\frac{d y}{d x}=0$ for maxima or minima
$\begin{aligned}
& \Rightarrow a \sin x=0 \Rightarrow x=\pi \\
& \therefore \left(\frac{d^2 y}{d x^2}\right)_{x=\pi}=a \cos \pi=-a
\end{aligned}$
$\therefore$ Function is maximum at $x=\pi$.
Hence, the correct answer is option: 'A'.