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  • Please Solve RD Sharma Class 12 Chapter 17 Maxima and Minima Exercise Case Study Based Questions question 1 subquestion (iii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 17 Maxima and Minima Exercise Case Study Based Questions question 1subquestion (iii) Maths Textbook Solution.

Answers (1)

Answer:  \frac{5000}{\pi} \mathrm{m}^{2}

Hint: use maxima minima concept.

Solution:

Now,  A=\frac{2}{\pi}(100 x-x^2)
To find maximum value of A we find

\frac{\mathrm{dA}}{\mathrm{dx}}

We must show f’(x) = 0 for finding maxima and minima

\begin{aligned} &\frac{d A}{d x}=\frac{2}{\pi}(100-2 x) \\ & \end{aligned}

\frac{d A}{d x}=0 \\

\frac{2}{\pi}(100-2 x)=0 \\

100=2 x \\

x=50

Putting x value in A

\begin{aligned} A &=\frac{2}{\pi}\left(100 \mathrm{x}-\mathrm{x}^{2}\right) \\ \end{aligned}

=\frac{2}{\pi}\left(100 \times 50-(50)^{2}\right) \\

=\frac{2}{\mathrm{~T}}(5000-2500) \\

\mathrm{A} . =\frac{2}{\pi}(2500)=\frac{5000 \mathrm{~m}^{2}}{\pi}

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