What is the maximum value of the function f(x) = 4 sin2 x + 1?

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Option 1 : 5
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Detailed Solution

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Calculation:

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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