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Question
Find the maximum and minimum value, if any, of the following function given by f(x) = |sin 4x + 3|
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Solution
Given function f(x) = |sin 4x + 3|
Maximum value of sin 4x = 1
∴ Maximum value of f(x) = |sin 4x + 3|
3 -1 ≤ sin 4x + 3 ≤ ; 1 + 3 ∀ x ∈ R.
|2| ≤ lsin 4x + 3 |≤| 4 | ∀ x ∈ R.
And Minimum value of sin 4x = - 1
Minimum value of f(x) = |sin 4x + 3|
= `abs (-1 + 3) = 2`
Minimum value off (x) = 2, which occurs when sin 4x = -1, and maximum value of f (x) = 4, which occurs when sin 4x = l.
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