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Question
Find the maximum and minimum value, if any, of the following function given by h(x) = sin(2x) + 5.
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Solution
Given function h(x) = sin (2x) + 5
We know that -1 ≤ sin 2x ≤ 1
⇒ 4 ≤ 5 + sin 2x ≤ 6
Maximum value of sin 2x = 1
∴ h(x) = Maximum value of sin 2x + 5, 1 + 5 = 6
Minimum value of sin 2x = - 1
∴ h(x) = Minimum value of sin 2x + 5 = -1 + 5 = 4
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