posted by Cris on .
I'm trying to finish up my pre-cal homework and I am stuck on 2 problems...
***determine the intervals over which the function is increasing, decreasing, or constant***
33. f(x)=√x^2-1 (that's square root of x^2-1)
thank you so much for the help =)
Hmmm. Since this is pre-cal, are you allowed to use derivatives? Assuming yes, then we have
32. f' = 2x-4
f' <0 for x<2 so f is decreasing on (-oo,2)
f' > 0 for x>2, so f is increasing on (2,+oo)
f' = 0 at x=2, so f is not increasing or decreasing there.
33. f' = x/sqrt(x^2-1)
f is undefined for -1 <= x <= 1
f' > 0 for x > 1 so f is increasing on (1,+oo)
f' < 0 for x < -1 so f is decreasing on (-oo,-1)
Use a graphing tool to verify this visually.