EXAM Find the local minimum and maximum values of the function below. f(x) = 3x4 – 8x3 – 210x2 + 5 Video Example SOLUTION f'(x) 12x3 - 24x2 - 420x = 12x(x – 7)(x + 5) From the chart Interval 12x x - 7 x + 5| f'(x) f x < -5 decreasing on (-∞, -5) -5 < x < 0 increasing on (-5, 0) 0 < x < 7 decreasing on (0, 7) + + x > 7 + + increasing on (7, 0) we see that f'(x) changes from negative to positive at -5, so is a local minimum value by the First Derivative Test. f(-5) = Similarly, f'(x) changes from negative to positive at 7, so f(7) = is a local minimum value.

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