Question
Download Solution PDFWhat is the maximum value of the function f(x) = 4 sin2 x + 1?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given: f(x) = 4 sin2 x + 1
To find: Maximum value of f(x)
We know that, range of sin x is [-1, 1], i.e.,
-1 ≤ sin x ≤ 1
Squaring the equalities, we get,
⇒ 0 ≤ sin2 x ≤ 1
⇒ 0 ≤ 4sin2 x ≤ 4
⇒ 1 ≤ 4sin2 x + 1 ≤ 5
⇒ 1 ≤ f(x) ≤ 5
Hence, maximum value of f(x) is 5.
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