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  • Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 14 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 14 maths textbook solution

Answers (1)

Answer:

              1

Hint:

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

Given:

Sum of two non-zero numbers is 4

Solution:

Let us consider

              x+y=4

Or          y=4-x

That is

\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}

Or f\left ( x \right )=\frac{4}{xy}=\frac{4}{x\left ( 4-x \right )}          

Now

\begin{aligned} &f(x)=\frac{4}{\left(4 x-x^{2}\right)} \\ &f^{\prime}(x)=\left(\frac{-4}{\left(4 x-x^{2}\right)^{2}}\right)(4-2 x) \end{aligned}

Substituting {f}'\left ( x \right )  we get 4-2x=0

{f}'\left ( x\therefore x=2,y=2 \right )

Therefore

\begin{aligned} &\min \left(\frac{1}{x}+\frac{1}{y}\right)=\frac{1}{2}+\frac{1}{2} \\ &\min \left(\frac{1}{x}+\frac{1}{y}\right)=1 \end{aligned}

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