Question

 Find the maximum and minimum values, if any, of the following functions given by

(iii) f(x) = −(x − 1)² + 10

Answer 1

(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.