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  • Please solve rd sharma class 12 Chapter 17 Maxima and Minima excercise 17 point 3 question 1 sub-question 10 maths textbook solution

Please solve rd  sharma class 12 Chapter 17 Maxima and Minima excercise 17.3  question 1 sub-question 10  maths textbook solution

Answers (1)

Answer:

Point of local minima value is a and it’s local minimum value is 2a. Also point of local maxima is -a and it’s local maximum value is  -2a

Hint:

First find critical values of f(x) by solving f'(x) =0 then find f''(x).

If f''(c_1) >0 then c_1 is point of local minima.

If  f''(c_2) <0 then c_2 is point of local maxima .

where c_1  &c_2 are critical points.

Put c_1 and c_2 in f(x) to get minimum value & maximum value.

Given:

f(x)=x+\frac{a^{2}}{x}, a>0

Explanation:

We Have,

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

For maxima and minima ,f’(x)=0

\begin{aligned} 1-\frac{a^{2}}{x^{2}} &=0 \\ x &=\pm a \end{aligned}

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