Find where the function f(x) 3x4 8x 144x 9 is increasing and where it is decreasing 4 2000 4000 6000 8000 4 6 8 f'(x) 12x 24x 288x 12x(x )(x To use the I D Test, we have to know where f'(x) 0 and where f'(x) 0 This depends on the signs of the three factors of f'(x), namely, 12x, x intervals whose endpoints are the critical numbers and We divide the real line into (smallest), 0, and (largest) and arrange our work in a chart A plus sign indicates that the given expression is positive, and a negative sign indicates that it is negative The last column of the chart gives the conclusion based on the I D Test For instance, f'(x) 0 for 0 x 6, so f is Select an answer on (0, 6) (It would also be true to say that fis decreasing on the closed interval 0, 6 ) Interval 12x HA 4 0 x 6x 4 f'(x) f decreasing on ( 0, 4) Select an answer on (4,0)

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Find where the function f(x) = 3x4 - 8x- 144x + 9 is increasing and where it is decreasing. -4 -2000- -4000 -6000- -8000

Find where the function f(x) = 3x4 - 8x- 144x + 9 is increasing and where it is decreasing. -4 -2000- -4000 -6000- -8000 4 6 8 f'(x) = 12x-24x - 288x = 12x(x- )(x+ To use the I/D Test, we have to know where f'(x) > 0 and where f'(x)

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