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I understand the first-order derivative (or partial derivative) tells you the slope of the tangent line at that point. If this is the case, what does second-order derivative tell you about?

Thank you

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  • $\begingroup$ concavity: if it is concave up or concave down (you are familiar with this through open upwards and downwards parabolas) $\endgroup$ – user29418 Feb 13 '18 at 21:31
  • $\begingroup$ Right. I just remember now. Thank you $\endgroup$ – Katherine Feb 13 '18 at 21:32
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Second derivative is related to rate of change and slope of first derivative that is convexity/concavity of the function, notably if

  • $f''(x)\ge 0\implies f(x)$ is convex
  • $f''(x)\le 0 \implies f(x)$ is concave

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