Finding local maximum and minimum values

Question

Assignment:

Q1) Find the local maximum and minimum values and saddle point(s). Here is the function:

f(x,y) = x³y + 12x² -8y

Q2) Use Lagrange multiplier to find the extreme values (i.e. the max and min) of:

f(x,y) = 4x+6y

subjected to the constraint

x² + y² = 13

Provide complete and step by step solution for the question and show calculations and use formulas.