Determine the location of each local extremum of the function.
-$f(x)=\frac{x^{4}}{4}-\frac{4}{3} x^{3}-\frac{9}{2} x^{2}+36 x+4$
A) Local maxima at -3 and 4 ; local minimum at 3
B) Local maximum at -3 ; local minimum at 4
C) Local maxima at 3 and -4 ; local minimum at 3
D) Local maximum at 3 ; local minima at -3 and 4

Question

Quizplus · Accepted Answer

The first derivative test shows that $f'(x)$ changes from positive to negative at $x=3$, indicating a local maximum, and from negative to positive at $x=-3$ and $x=4$, indicating local minima.

Determine the Location of Each Local Extremum of the Function f(x)=x44−43x3−92x2+36x+4f(x)=\frac{x^{4}}{4}-\frac{4}{3} x^{3}-\frac{9}{2} x^{2}+36 x+4f(x)=4x4​−34​x3−29​x2+36x+4

Determine the Location of Each Local Extremum of the Function $f(x)=\frac{x^{4}}{4}-\frac{4}{3} x^{3}-\frac{9}{2} x^{2}+36 x+4$