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Calculus

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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***

32. f(x)=x^2-4x

33. f(x)=√x^2-1 (that's square root of x^2-1)

thank you so much for the help =)

  • Calculus - ,

    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.

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