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

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

Question

Identify intervals on which the function is increasing, decreasing, or constant. 

g(x) = 1 - (x - 6)2

loser66 · Answer

calculate g'(x) , let it =0 to get the value of critical points. Plug each of them into g(x) to find value of g(x) at those points. Then, compare them, make table to know in which interval it increasing/decreasing /saddle.

anonymous · Answer

Is it -6 or +6 in the answer?

loser66 · Answer

@cwrw238

cwrw238 · Answer

can you find g'(x) or do you need help?

anonymous · Answer

Well, I know its going to be either increasing <-6 and decreasing > - 6 or increasing < 6 and decreasing > 6

cwrw238 · Answer

g'(x) = -2(x - 6) = 0    at critical points

x - 6 = 0
x = 6
to find if this is a maximum or a minimum  we find g"(x)

this = -2  
negative gives a maximum

so its is increasing for x < 6, maximum at x = 6 and decreasing for x > 6

anonymous · Answer

Thanks!

cwrw238 · Answer

http://www.wolframalpha.com/input/?i=y+%3D+1+-+%28x+-+6%29%5E2

cwrw238 · Answer

yw