The rule of the derivative of a function $f$ is given. Find the location of all local extrema.
-$f^{\prime}(x)=\left(x^{2}-1\right)(x+3)$
A) Local maxima at -3 and 1 ; local minimum at -1
B) Local maximum at $-3+\sqrt{8}$; local minimum at $-3-\sqrt{8}$
C) Local maximum at -1 ; local minima at -3 and 1
D) Local maximum at $-3-\sqrt{8}$; local minimum at $-3+\sqrt{8}$

Question

Quizplus · Accepted Answer

The critical points are found by setting $f'(x) = 0$, which gives $x = -3, -1, 1$. Testing intervals around these points shows a local maximum at $x = -1$ and local minima at $x = -3$ and $x = 1$.

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