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Single variable calculus question. (first post)

  1. Nov 12, 2003 #1
    Hi I'm new to this forum.
    I was wondering if anyone can explain to me how to do a first derivative test to find the relative extrema. I've been trying to read it, but it just isn't sinking in. thanks in advanced.
  2. jcsd
  3. Nov 12, 2003 #2


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    If a function is continuous and differentiable then local maximums amd minimums occur where the graph of a function is flat, so they occur where the derivative is zero.

    So, when looking for maximums and minimums you only need to check endpoints, and points where the derivative is zero or doesn't exist.
  4. Nov 13, 2003 #3


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    There is third possibility for zero derivative points, horizontal inflection point. Example y=x3, at x=0.
  5. Nov 14, 2003 #4
    thanks a lot guys. appreciate the help.
  6. Nov 14, 2003 #5
    please open the attachment below, to get better picture...
    (note : that the picture is the graph f(x) against x )

    actually to see the better idea of first derivative by imagining it as a gradient of the graph of a fuction.

    suppose I have fuction f(x)

    when you derive it becomes f'(x)...
    what is f'(x) ???

    f'(x) is the gradient.....

    now look at the picture that there are 3 red straight lines.you can get line straight ,if and only if at the turning point like what you see in the graph

    at the other point you will find the line is slope like both the blue line.

    remember that straight line has gradient 0....that is to say, f'(x)=0

    so to find either maxima or minima ,you must find value of x ,which can be subtituted into f'(x) and get value 0.

    Attached Files:

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