Q1a) Find the critical points and classify them as local maximum, local minimum, saddle points or "cant tell".

f(x,y,z)= x^2 +12xy +y^2-3yz+4z^2 +x+y+z

b) Sketch the shape of five standard quadratic forms that are positive definite, negative definite, positive semi definite, negative semi definite and indefinite form.