Question
Find the local maxima or local minima, if any, of following functions using the first derivative test only. Find also the local maximum and the local minimum values, as the case may be:
Solution
Let f (x) = (x – 3)4.
∴ f ' (x) = 4 (x – 3)3
Now f ' (x) = 0 ⇒ 4(x – 3)3 = 0 ⇒ (x– 3)3 = 0 ⇒ x = 3
When x < 3 slightly, f ' (x) = – ve
When x > 3 slightly, f '(x) = + ve
∴ at x = 3, f '(x) changes from – ve to + ve
∴ f (x) has local minima at x = 3
and this local minimum value = (3 – 3)4 = 0
