If a function has second derivative f ''(x) = $x ^ { 2 }$ ( $x ^ { 2 }$ - 4) is (0, 0) an inflection point?

Question

Quizplus · Accepted Answer

An inflection point occurs where the second derivative changes sign. The given second derivative $f''(x) = x^2(x^2 - 4)$ simplifies to $f''(x) = x^2(x + 2)(x - 2)$. The sign of $f''(x)$ does not change at $x = 0$; it remains positive for $x$ close to 0 (both just below and just above 0), indicating that (0, 0) is not an inflection point.

If a Function Has Second Derivative F ''(X) = x2x ^ { 2 }x2

If a Function Has Second Derivative F ''(X) = $x ^ { 2 }$