Question
Find the maximum and minimum values, if any, of the following functions without using the derivatives:
– (x – 2 )2 + 4
Solution
Let f (x) = – (x – 2)3 + 4
Now ( x – 2)2 ≥ 0 ∀ x ∊ R
⇒ – (x - 2)2 ≥ 0 ∀ x ∊ R ⇒ – (x – 2)2 + 4 ≤ 4 ∀ x ∊ R
∴ maximum value of f (x) is 4. It has no minimum value.
