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Math Help - Graph of function and derivative?

  1. #1
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    Graph of function and derivative?

    I have this question: Graph of function and derivative?-capture5.jpgand I'm struggling with it because I can't remember the rules for graphs of functions and what that means for their derivatives. I know some things but the continuous part is confusing me. Am I right? How would I figure this out? Thanks!
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  2. #2
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    Re: Graph of function and derivative?

    Only I and III are correct. Remember that when I have a pointy part in a graph, then there does not exist the derivative of that part of the function. Another way to look at it, is with the absolute value function, it might help clear a little any doubt due to this problem.
    This means that the derivative does not exist when x=b, but clearly the function is continuos, because if you were to draw the function with a pencil, it would not be necessary to lift the pencil in order to draw the whole function. The function is also differentiable in (a,b), this is because the point b is not included, so even though is not differentiable in b, it is in any other point close to it.

    I sure hope that this helps.
    Thanks from canyouhelp
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    Re: Graph of function and derivative?

    Quote Originally Posted by Yeison View Post
    Only I and III are correct. Remember that when I have a pointy part in a graph, then there does not exist the derivative of that part of the function. Another way to look at it, is with the absolute value function, it might help clear a little any doubt due to this problem.
    This means that the derivative does not exist when x=b, but clearly the function is continuos, because if you were to draw the function with a pencil, it would not be necessary to lift the pencil in order to draw the whole function. The function is also differentiable in (a,b), this is because the point b is not included, so even though is not differentiable in b, it is in any other point close to it.

    I sure hope that this helps.
    Thank you, this really helps!
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