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Math Help - Increasing or Decreasing Functions at an x value

  1. #1
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    Increasing or Decreasing Functions at an x value

    I missed a math class and I really don't know where to start with this. Here are some examples of the problems, I just need an idea of the process here.

    We just did derivatives, so I know how to do that. I've found a lot of information on how to find the intervals of where a function is increasing or decreasing, but not with an x value already given.

    Determine if the function is increasing or decreasing at x=2.

    1. f(x) = x^3 - 7x + 1

    2. f(x) = (x - 3)^4

    3. f(x) = cubed root of (x - 1)

    4. f(x) = (x + 1)/(x - 2)

    Thanks in advance!!!
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  2. #2
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    Quote Originally Posted by ktprieto View Post
    I missed a math class and I really don't know where to start with this. Here are some examples of the problems, I just need an idea of the process here.

    We just did derivatives, so I know how to do that. I've found a lot of information on how to find the intervals of where a function is increasing or decreasing, but not with an x value already given.

    Determine if the function is increasing or decreasing at x=2.

    1. f(x) = x^3 - 7x + 1

    2. f(x) = (x - 3)^4

    3. f(x) = cubed root of (x - 1)

    4. f(x) = (x + 1)/(x - 2)

    Thanks in advance!!!
    Find f'(x) and use it to calculate f'(2). If f'(2) > 0 then the function is increasing at x = 2. If f'(2) < 0 then the function is decreasing at x = 2.

    Note that the function in question 4 is not defined at x = 2 (why?).
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    Quote Originally Posted by ktprieto View Post
    We just did derivatives, so I know how to do that. I've found a lot of information on how to find the intervals of where a function is increasing or decreasing, but not with an x value already given.
    If the derivative at the point is positive, then the function is increasing at that point. If it is negative, the function is decreasing.
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