Posted by Cris on Saturday, September 17, 2011 at 9:02pm.
I'm trying to finish up my precal homework and I am stuck on 2 problems...
***determine the intervals over which the function is increasing, decreasing, or constant***
32. f(x)=x^24x
33. f(x)=√x^21 (that's square root of x^21)
thank you so much for the help =)

Calculus  Steve, Wednesday, September 21, 2011 at 4:24pm
Hmmm. Since this is precal, are you allowed to use derivatives? Assuming yes, then we have
32. f' = 2x4
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^21)
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.
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