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  • Provide solution for rd sharma class 12 chapter 17 Maxima and Minima excercise 17.1 question 2

Provide solution for rd sharma class 12 chapter 17 Maxima and Minima excercise 17.1 question 2

Answers (1)

best_answer

Maximum value is 2 and minimum value does not exist.

Hint:

f(x) have max value in [a, b] such that f(x) ≤ f(c) for all x belongs to [a ,b] and if f(x) ≥ f(c) then f(x) has minimum value.

Given:

f(x)=-(x-1)^{2}+2 \text { on } R

Explanation:

f(x)=-(x-1)^{2}+2

We can see that,

\begin{aligned} &(x-1)^{2} \geq 0 \text { for every } x \in R \\ &-(x-1)^{2} \leq 0 \\ &-(x-1)^{2}+2 \leq 2 \text { for every } \mathrm{x} \in R \end{aligned}

So, the maximum value of f is attained when (x-1) = 0

x-1 = 0

x = 1

Thus, maximum value of f(x) = f(1)

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

Therefore, maximum value is 2 and it does not have minimum value.

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