Find the maximum and minimum values, if any, of the following function given by,

$h (x) = s i n (2 x) + 5$

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Solution

Given function is, $h (x) = s i n 2 x + 5$
We know that, $- 1 \leq s i n x \leq 1 \Rightarrow - 1 \leq s i n 2 x \leq 1$
$\Rightarrow - 1 + 5 \leq s i n 2 x + 5 \leq 1 + 5 \Rightarrow 4 \leq s i n 2 x + 5 \leq 6$
Hence, maximum value of h(x) is 6 and minimum value of h(x) is 4.

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