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