Question

Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 1 - (x - 7)2

Increasing: x < 7; decreasing: x > 7
Increasing: x < -7; decreasing: x > -7
Increasing: x > 1; decreasing: x < 1
Increasing: x < 1; decreasing: x > 1

Answer 1

Increasing in x < 7 and decreasing in x > 7.

Explanation:

g(x) = 1 -
`(x-7)^(2)`

`(dg(x))/(dx) = -2(x - 7)`

If a function is increasing in a interval, its first derivative is positive and if a function is decreasing in an intreval, its first derivative is negative.

Using this concept here,

Substitute x > 7,

the first derivative is negative.Hence it is decreasing in this interval.

Substitute x < 7,

The first derivative is positive.Hence it is increasing in this interval.

Hence the answer is increasing in x < 7 and decreasing in x > 7.