F(x)=6x3−54x2−126x−8 is decreasing on the interval ( equation editorequation editor , equation editorequation editor ). it is increasing on the interval ( −[infinity], equation editorequation editor ) and the interval ( equation editorequation editor , [infinity] ).

The function is decreasing on the interval and it is increasing on the interval

Step-by-step explanation:

To determine the intervals of increase and decrease of the function , perform the following steps:

1. Differentiate the function

2. Obtain the roots of the derivative, f'(x) = 0

3.  Form open intervals with the roots of the derivative and take a value from every interval and find the sign they have in the derivative.

If f'(x) > 0, f(x) is increasing.

If f'(x) < 0, f(x) is decreasing.

On the interval , take x = -2,

 f'(x) > 0 therefore f(x) is increasing

On the interval , take x = 0,

 f'(x) < 0 therefore f(x) is decreasing

On the interval , take x = 10,

 f'(x) > 0 therefore f(x) is increasing

The function is decreasing on the interval and it is increasing on the interval

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step-by-step explanation: