If the second derivative of a function is $f ^ { \prime \prime } ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$ is (2, f(2)) an inflection point'

Question

Quizplus · Accepted Answer

An inflection point occurs where the second derivative changes sign. The given second derivative $f''(x) = (x - 2)^2(x^2 - 9)$ does not change sign at $x = 2$ because the factor $(x - 2)^2$ is always non-negative, and at $x = 2$, it is zero, making the second derivative non-positive on both sides of $x = 2$.

If the Second Derivative of a Function Is f′′(x)=(x−2)2(x2−9)f ^ { \prime \prime } ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)f′′(x)=(x−2)2(x2−9)

If the Second Derivative of a Function Is $f ^ { \prime \prime } ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$