Question

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

g(x) = 1 - (x - 6)^2

How would I solve this.

Answer 1

HI!!

Answer 2

do you recognize it as a parabola?

Answer 3

Hello, again.

Answer 4

Yes.

Answer 5

open up or down??

Answer 6

Up

Answer 7

hmmm

Answer 8

\[f(x)=-(x-6)^2+1\]

Answer 9

Oops, that's not what I graphed.

Answer 10

try it
you will see it opens down because the leading coefficient it negative

Answer 11

Yes, I forgot about the negative.

Answer 12

Alright, I have graphed it.

Answer 13

you can see that it has a maximum when x = 6
it is increasing from \(-\infty\) to \(6\) and decreasing after that

Answer 14

So, increasing x<6, decreasing x>6

Answer 15

yes

Answer 16

Thank you, Misty. You're very helpful.