The rule of the derivative of a function $f$ is given. Find the location of all local extrema.
-$\mathrm{f}^{\prime}(\mathrm{x})=(\mathrm{x}+5)(\mathrm{x}+2)(\mathrm{x}-4)$
A) Local maximum at -2 ; local minima at -5 and 4
B) Local maximum at 2 ; local minima at 5 and -4
C) Local maxima at 5 and -4 ; local minimum at 2
D) Local maxima at -5 and 4 ; local minimum at -2

Question

Quizplus · Accepted Answer

The derivative $\mathrm{f}^{\prime}(\mathrm{x})$ changes sign at the critical points $x = -5, -2, 4$. At $x = -2$, the derivative changes from positive to negative, indicating a local maximum. At $x = -5$ and $x = 4$, the derivative changes from negative to positive, indicating local minima.

The Rule of the Derivative of a Function fff Is Given Find the Location of All Local Extrema

The Rule of the Derivative of a Function $f$ Is Given Find the Location of All Local Extrema