Min f(x)
s.t.   Φ(x)

Max f(x)
s.t.   Φ(x)

Minimize[{x,(x^2)+(y^2) <1},{x,y}]

Minimize[{(x^2),x y==1},{x,y}]

Minimize[{(x^2)+(((y-1))^2),y>(x^2)},{x,y}]

FindMinimum[3(x^4)-28(x^3)+84(x^2)-96x+42,{x,1.1}]

Minimize[3(x^4)-28(x^3)+84(x^2)-96x+42,{x}]

Plot[3(x^4)-28(x^3)+84(x^2)-96x+42,{x,0,5}]

Summary of constrained optimization functions.