Determine the Location of Each Local Extremum of the Function $f(x)=x^{3}+\frac{7}{2} x^{2}+12 x+4$

Multiple Choice

Determine the location of each local extremum of the function.
- $f(x) =x^{3}+\frac{7}{2} x^{2}+12 x+4$

A) Local maximum at 3 ; local minimum at 4
B) Local maximum at -4 ; local minimum at -3
C) No local extrema
D) Local extremum at 3.5