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Question
Find the maximum and minimum value, if any, of the following function given by f(x) = −(x − 1)2 + 10
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Solution
We have, f (x) = 10 - (x - 1)2 for all x ∈ R
since, (x - 1)2 ≥ 0 ∀ x ∈ R
= - (x - 1)2 ≤ 0 ∀ x ∈ R
= 10 - (x - 1)2 ≤ ∀ x ∈ R
∴ Maximum f (x) = 10 which occurs when x - 1 = 0 i.e, when x = 1
f (x) has no minimum value for, f (x) → - ∞ As |x| →∞
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