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  • Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 15 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 15 maths textbook solution

Answers (1)

Answer:

              2

Hint:

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

Given:

x & y  are two real numbers such that x >0 and xy=1

Solution:

Let f\left ( x \right )=x+y  where xy=1

\begin{aligned} &f(x)=x+\frac{1}{x} \\ &f^{\prime}(x)=1-\frac{1}{x^{2}}=\frac{x^{2}-1}{x^{2}} \\ &f^{\prime \prime}(x)=\frac{2}{x^{3}} \end{aligned}

On putting {f}'\left ( x \right )=0  we get

x=\underline{+}1 butx> 0  (Neglecting x=-1 )

{{f}'}'\left ( x \right )> 0 forx=1

Hence f\left ( x \right )  attains minimum at x=1,y=1

\left ( x+y \right ) has minimum value 2

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