Find the maximum and minimum values, if any, of the function give… - Vidyadip

Question

Find the maximum and minimum values, if any, of the function given by:
h(x) = Sin (2x) + 5

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Answer

Given: $\text{h}\text{(x)} = \sin (2\text{x)} + 5\ \dots\text{(i)}$
Since $-1\leq\sin2\text{x}\leq 1\text{ for all } \text{x} \in \text{R}$
Adding 5 to all sides, $-1 + 5 \leq \sin 2\text{x} + 5\leq 1+ 5\ \Rightarrow 4\leq \text{h}\text{(x)} \leq6$
Therefore, minimum value of h(x) is 4 and maximum value is 6.

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