Question 10 Find the local minimum and maximum values of the function below f(x) 3x 12x 108x 6 f'(x) 12x 36x 216x 12x(x 6)(x 3) From the chart Interval 3 3 x 0 0 6 2 6 12x H T 6x 3 f'(x) f decreasing on (, 3) increasing on (3,0) decreasing on (0, 6) increasing on (6, 0) we see that f'(x) changes from negative to positive at 3, so f( 3) value by the First Derivative Test is a local minimum Similarly, f'(2) changes from negative to positive at 6, so f(6) is a local minimum value And, f(0) is a local maximum value because f'(x) changes from positive to negative at 0

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Question 10 < Find the local minimum and maximum values of the function below. f(x)=3x-12x- 108x + 6 f'(x)=12x-36x - 216x = 12x(x-6)(x+3) From

Question 10 < Find the local minimum and maximum values of the function below. f(x)=3x-12x- 108x + 6 f'(x)=12x-36x - 216x = 12x(x-6)(x+3) From the chart Interval

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