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  • Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 7 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 17 Maxima and Minima Exercise Fill in the blanks Question 7 maths textbook solution

Answers (1)

Answer:

              1

Hint:

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

Solution:

\begin{aligned} &f(x)=x+\frac{1}{x}\\ &f^{\prime}(x)=1-\left(\frac{1}{x^{2}}\right)\\ &\text { Put } f^{\prime}(x)=0\\ &1-\left(\frac{1}{x^{2}}\right)=0\\ &x=\pm 1\\ &f^{\prime \prime}(x)=\frac{2}{x^{3}}\\ \end{aligned}

\text { At } x=1, f^{\prime \prime}(x)=\text { Positive }\\

\text { At } x=-1, f^{\prime \prime}(x)=\text { Negative }\\

f(x) \text { Attains minimum value at } x=1

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