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

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

Answers (1)

Answer:

              \left ( 3,19 \right )

Hint:

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

Given:

 f\left ( x \right )=\left ( x-1 \right )^{2}

Solution:

f\left ( x \right ) is the sum of a square and a constant term. It will acquire minimum value when the square term becomes zero

Hence

f\left ( x \right ) is max at x=-3

f\left ( -3 \right )=19

Or

\begin{aligned} &f^{\prime}(x)=(x-1)^{2}+1 \\ &f^{\prime}(x)=2(x-1)=0 \\ &x \in[-3,1] \end{aligned}

\begin{aligned} &f^{\prime}(x)=2> 0 \end{aligned}

x=1 is local minimum

\begin{aligned} &f^{\prime \prime}(x)=2>0\\ &x=1 \text { is local minimum }\\ &f(-3)=(-3-1)^{2}+3\\ &=19(m, M)\\ &=(3,19)\\ &f(1)=3 \rightarrow \min =m \end{aligned}

 

 

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