Example 2 find the local minimum and maximum values of the function below. f(x) = 3x4 − 16x3 − 270x2 + 3 video example solution f '(x) = 12x3 − 48x2 − 540x = 12x(x − 9)(x + 5) from the chart interval 12x x − 9 x + 5 f '(x) f x < −5 − − − − decreasing on (−∞, −5) −5 < x < 0 − − + + increasing on (−5, 0) 0 < x < 9 + − + − decreasing on (0, 9) x > 9 + + + + increasing on (9, ∞) we see that f '(x) changes from negative to positive at −5, so f(−5) = 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.