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Question
Find the maximum and minimum value, if any, of the following function given by f(x) = (2x − 1)2 + 3.
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Solution
We have, f(x) = (2x - 1)2 + 3 for all x ∈ R.
Since, (2x - 1)2 ≥ 0
= (2x - 1)2 + 3 ≥ 3
∴ Minimum f (x) = 3, which occurs when 2x - 1 = 0 i.e, when x = `1/2`
Value of f (x) has no maximum value, because f (x) → ∞ as |x| → ∞
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