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

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.