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If the second derivative of a function is constant on some interval, you can bound the maximum of this function's absolute value from below in terms of this constant.

What does the above statement mean?

If $f(x)=ax^2+bx+c\implies f''(x)=2a$

Does the above statement mean $|f(x)|\ge2a?$

My main intention is to understand the answer posted on this thread.

Arctic Char
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aarbee
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    For $f(x) = x^2$, $a=1$ but $|f(0)| = 0 < 2= 2a$, so your claim is false. Also, its absolute value is unbounded so there is no maximum value. – Didier Jun 20 '21 at 11:45
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    It says "in terms of this constant", no "by this constant". – jjagmath Jun 20 '21 at 11:48

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