Question

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

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

Answer 1

are you in a calculus class?

Answer 2

yes!

Answer 3

ok, then you probably want to find the second derivative first, because there is a second derivative test which will tell you if the function is increasing or decreasing.

Answer 4

okay.. then what?

Answer 5

I figured it out

Answer 6

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


d/dx(g(x)) = -2(x-7)

d/dx(-2(x-7)) = -2


http://en.wikipedia.org/wiki/Second_derivative_test

if the second derivative is less than 0 then the function is concave down. since this is a parabola, it is always concave down as seen in this graph.

http://www.wolframalpha.com/input/?i=g%28x%29+%3D+1+-+%28x+-+7%29%5E2

however, you are asking when it is increasing and where it is decreasing

for that we need the first derivative. set it equal to zero to find the x value where the function is a maximum

-2(x-7) = 0

-2x + 14 = 0

-2x = -14

x = 7

the function is increasing from (-infinity,7) and decreasing from (7 to infinity).

a good video to learn more about this: http://www.youtube.com/watch?v=g8Nv7Gap2Z8