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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- Mar 23rd 2014, 02:35 PMstateSecond 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!

- Mar 23rd 2014, 04:25 PMromsekRe: Second Derivative
the first derivative, h'(x), will be monotonically increasing on that interval.

- Mar 23rd 2014, 05:09 PMPlatoRe: Second Derivative
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 $h'(x)=e^{-x}~?$. - Mar 23rd 2014, 06:20 PMromsekRe: Second Derivative
ignore post #2. It's incorrect.