Question

The function W=Z^4-Z^3/3 has a(n);
1.minimum at Z=0 and a maximum at Z=¼
2.minimum at Z=0 and a point of inflection at Z=¼
3.maximum at Z=0 and a minimum at Z=¼
4.point of inflection at Z=0 and a minimum at Z=1/4

Answer 1

dw/dz= 4z^3-z2=0
z=0, z=1/4.
w''= 12z^2-2z=0, when we plug z=0,
and negative when plug z=1/4.
maximum at z=1/4. and neither maximum nor minimum at z=0