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  • Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 3 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 3 maths textbook solution

Answers (1)

Answer:

              \sqrt{2}

Hint:

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

Given:

f\left ( x \right )=\sin x+\cos x

Solution:

\begin{aligned} &f(x)=\sin x+\cos x \\ &\frac{d}{d x}=(f(x))=\cos x-\sin x \end{aligned}                                   [\frac{d}{d x}(\sin x)=\cos x ; \frac{d}{d x}(\cos x)=-\sin x ]

{f}'\left ( \cos x-\sin x \right )\rightarrow {f}'\left ( x \right )=0 for Maxima

{{f}'}'\left ( x \right )=-\left ( \sin x+\cos x \right )

Therefore

\sin x=\cos x and\tan x=1

\begin{aligned} &x=\frac{\pi}{4} \\ &f(x) \Rightarrow \max \text { at } \frac{\pi}{4} \\ &f(x)=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}} \\ &f(x)=\sqrt{2} \end{aligned}

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