The rule of the derivative of a function $f$ is given. Find the location of all points of inflection of the function $f$.
-$f^{\prime}(x)=(x-2)(x-4)(x-5)$
A) $2,4,5$
B) 3.67
C) 4
D) $\frac{11-\sqrt{7}}{3}, \frac{11+\sqrt{7}}{3}$

Question

Quizplus · Accepted Answer

Points of inflection occur where the second derivative changes sign. First, find the second derivative of $f$ by differentiating $f'(x) = (x-2)(x-4)(x-5)$. Then, solve $f''(x) = 0$ to find potential inflection points. The correct solutions are $\frac{11-\sqrt{7}}{3}$ and $\frac{11+\sqrt{7}}{3}$.

The Rule of the Derivative of a Function fff Is Given Find the Location of All Points of Inflection of Given

The Rule of the Derivative of a Function $f$ Is Given Find the Location of All Points of Inflection of Given