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  • Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 2 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 2 maths textbook solution

Answers (1)

Answer:

              -1

Hint:

For maxima or minima we must have {f}'\left ( x \right )=0

Given:

f(x)=\sin x\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]f(x)=\sin x\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]

Solution:

\begin{aligned} &f(x)=\sin x \\ &f^{\prime}(x)=\cos x \end{aligned}

For maxima and minima

\begin{aligned} &f^{\prime}(x)=0 \\ &\cos x=0, x=\frac{\pi}{2},-\frac{\pi}{2} \\ &f^{\prime \prime}(x)=-\sin x>0 \end{aligned}                     Whenx=\frac{\pi}{2} 

Now

f^{\prime \prime}\left ( \frac{\pi}{2} \right )=\sin \left ( -\frac{\pi}{2} \right )

                 =-\sin\frac{\pi}{2}

                 = -1

Hence Minimum value of

f(x)=\sin x \quad \text { in }-\frac{\pi}{2} \leq x \leq \frac{\pi}{2} \text { is }-1 

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