Find the maximum and minimum values, if any, of the following functions given by
(iii) f(x) = −(x − 1)2 + 10
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(iii) The given function is f(x) = − (x − 1)2 + 10.
It can be observed that (x − 1)2 ≥ 0 for every x ∈ R.
Therefore, f(x) = − (x − 1)2 + 10 ≤ 10 for every x ∈ R.
The maximum value of f is attained when (x − 1) = 0.
(x − 1) = 0 ∴ x = 0
∴Maximum value of f = f(1) = − (1 − 1)2 + 10 = 10
Hence, function f does not have a minimum value.
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