Question
Find the maximum and minimum values, if any, of the following functions without using the derivatives:
(2 x – 1)2 + 3
Solution
Let f (x) = (2 x – 1)2 + 3
Now (2 x – 1)2 ≥ 0 ∀ x ∊ R
⇒ (2 x – 1)2 + 3 ≥ 3 ∀ x R
∴ minimum value of f (x) is 3. It has no maximum value.
