Determine the critical points of each of the following functions and characterize each as a minimum, maximum or saddle point.

a$.f(x)=x^3+6x^2-15x+2$

b$.f(x)=2x^3-25x^2-12x+15$

c$.f(x,y)=x^2-4xy+y^2$

d$.f(x,y)=x^4-4xy+y^4$