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

Multiple Choice

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