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Provide solution for rd sharma class 12 chapter 17 Maxima and Minima  excercise 17.1 question 1

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Answer:

Maximum value is 4 and minimum value is 2.

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)=|\sin 4 x+3|

Explanation:

We have,

f(x)=|\sin 4 x+3|

We know,

\begin{aligned} &-1 \leq \sin 4 x \leq 1\\ &-1+\underline{3} \leq \sin 4 x+3 \leq 1+3\\ &\underline{2} \leq \sin 4 x+3 \leq 4\\ &\underline{2} \leq|\sin 4 x+3| \leq 4 \end{aligned}

So maximum value is 4 and minimum value is 2.

 

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