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

Question

Find the maximum and minimum values, if any, of the following functions given by f (x) = (2x – 1) 2 + 3

Philoid · Accepted Answer

It is given that f (x) = (2x – 1)² + 3

Now, we can see that (2x – 1)² ≥ 0 for every x ϵ R

⇒ f (x) = (2x – 1)² + 3 ≥ 3 for every x ϵ R

The minimum value of f is attained when 2x – 1 = 0

2x -1 = 0

Then, Minimum value of

Therefore, function f does not have a maximum value.