Question

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

Answer 1

Answer:

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

Step-by-step explanation:

g(x) = 1 - $(x-7)^{2}$

$\frac{dg(x)}{dx} = -2(x - 7)$

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.