Question

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

(i) f(x) = (2x − 1)² + 3          

Answer 1

(i) The given function is f(x) = (2x − 1)² + 3.
It can be observed that (2x − 1)² ≥ 0 for every x ∈ R.
Therefore, f(x) = (2x − 1)² + 3 ≥ 3 for every x ∈ R.
The minimum value of f is attained when 2x − 1 = 0.

Hence, function f does not have a maximum value.