Find the maximum or minimum values, if any, without using derivat… - Vidyadip

Question

Find the maximum or minimum values, if any, without using derivatives, of the function $f(x)=|\sin 4 x+3|$

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Answer

Maximum value $= 4,$ Minimum value $= 2$
We know that
$-1 \leq \sin \theta \leq 1$
$\therefore-1 \leq \sin 4 x \leq 1$
Adding $3,$ on both sides, of above
We get
$-1+3 \leq \sin 4 x+3 \leq 1+3$
$2 \leq|\sin 4 x+3| \leq 4$
Hence $\min.$ Value is $2$ and $\text{max}$ value is $4$.

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