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Math Help - Second Derivative

  1. #1
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    Second Derivative

    If the second derivative is continually increasing over the interval [-2,1] on h(x), what does that tell us about the first derivative, h'(x)? Thanks!
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  2. #2
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    Re: Second Derivative

    the first derivative, h'(x), will be monotonically increasing on that interval.
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  3. #3
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    Re: Second Derivative

    Quote Originally Posted by state View Post
    If the second derivative is continually increasing over the interval [-2,1] on h(x), what does that tell us about the first derivative, h'(x)?
    Consider the function: $h(x)=-e^{-x}$. See its plot here.

    Please note that $h(x)=h''(x)$, hence the second derivative is increasing on $[-2,1]$ but what about $h'(x)=e^{-x}~?$.
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    Re: Second Derivative

    ignore post #2. It's incorrect.
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