Question

The function $y=a(1–\cos x)$ is maximum when $x=$

• A. $\mathrm{\pi }$
• B. $\frac{\mathrm{\pi }}{2}$
• C. $-\frac{\mathrm{\pi }}{2}$
• D. $-\frac{\mathrm{\pi }}{6}$

Answer 1

The correct option is A

$\mathrm{\pi }$

Find the value of $x$ when the given function is maximum

Given, $y=a(1–\cos x)$

On differentiating w.r.t. $x$,we get

$y\text{'}=a\sin x$

Put $y\text{'}=0$ for maxima or minima

$$\begin{gathered} \sin x=0 \\ \Rightarrow x=0,\mathrm{\pi } \end{gathered}$$

Again differentiating w.r.t. $x$,we get

$$\begin{gathered} y\text{'}\text{'}=a\cos x \\ \Rightarrow y\text{'}\text{'}\left(0\right)=aandy\text{'}\text{'}\left(\mathrm{\pi }\right)=-a \end{gathered}$$

As,$y\text{'}\text{'}\left(\mathrm{\pi }\right)<0$

Therefore, $y$ is maximum when $x=\mathrm{\pi }$

Hence, option (A) $\mathrm{\pi }$, is the correct answer.