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I recently learned about the concept of the 2ns derivative test, and while solving some sums I encountered some functions which had a constant 2nd derivative. Now I made a simple inference that it means that the function has only one out of the two extremes. Is there any other inference we can make as well, given a constant value for the 2nd derivative test?

Ethan Bolker
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divyam sureka
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  • If the second derivative is constant, can you integrate it and say something about the first? Once you've done that, can you say anything about the function itself? – Aryaman Maithani May 22 '20 at 19:16
  • Acceleration due to gravity is a constant: -9.8 m /s^2. So the kind of curves you get are those that look like an arc made when you throw a ball in the air - parabolas. – Jair Taylor May 22 '20 at 19:20

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Hint. You could start by thinking about whether you know any functions with a constant second derivative.

Hint. You know (or should) that a function with a constant first derivative is linear. Can you use that to figure out what a function with a constant second derivative must be?

Ethan Bolker
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