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Math Help - Questions about relative extremas?

  1. #1
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    Questions about relative extremas?

    -Are critical points when the function is equal to zero?
    -What is the difference of relative and absolute extrema? Is relative extrema is when the derivative is zero and the absolute extrema when the 2nd derivative = 0??
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  2. #2
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    Critical points exist when the derivative of the function equals to 0 or undefined.

    I'm not sure how to explain relative and absolute extrema, but I will try my best.

    Relative extrema occurs when the derivative=0 and it changes sign around that x value.

    Absolute extrema is basically the highest or lowest value on the graph.

    The second derivative is used to test concavity.
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  3. #3
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    So if the critical point the derivative is 1, does that mean it will be (1, 0) on the function? Or (1, 0) on the derivative graph?
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  4. #4
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    If the critical point of a function occurs at x=1, that means the slope or derivative (slope=derivative) of the original function is 0 at x=1.

    It does not imply that (0,1) or (1,0) will be points on the graph.
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  5. #5
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    Advice helped me alot during my test today.. I know I probably didn't get a 100% on it, but when we got the the relative extrema part, the only hard part I had difficulty on was curve sketching(whihc I know I got wrong) and some chart thingy.. Thanks.
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