Example 2 find the local minimum and maximum values of the function below. f(x) = 3x4 â 16x3 â 270x2 + 3 video example solution f '(x) = 12x3 â 48x2 â 540x = 12x(x â 9)(x + 5) from the chart interval 12x x â 9 x + 5 f '(x) f x < â5 â â â â decreasing on (ââ, â5) â5 < x < 0 â â + + increasing on (â5, 0) 0 < x < 9 + â + â decreasing on (0, 9) x > 9 + + + + increasing on (9, â) we see that f '(x) changes from negative to positive at â5, so f(â5) = 840 changed: your submitted answer was incorrect. your current answer has not been submitted. is a local minimum value by the first derivative test. similarly, f '(x) changes from negative to positive at 9, so f(9) = -11512 incorrect: your answer is incorrect. is a local minimum value. and, f(0) = 3 correct: your answer is correct. is a local maximum value because f '(x) changes from positive to negative at 0.