Question

Problem 2

Find the locations and values for the maximum and minimum of f (x, y) = 3x^3 − 2x^2 + y^2 over the region given by x^2 + y^2 ≤ 1.

and then over the region x^2 + 2y^2 ≤ 1.

Use the outline:

INSIDE

Critical points inside the region.

BOUNDARY

For each part of the boundary you should have:

• The function g(x, y) and ∇g

• The equation ∇f = λ∇g
• The set of three equations in three unknowns and their complete solution set

• The list of endpoints of that boundary component (if necessary)

COMPARE

Finally, you compute the value of f(x,y) at each point you have identified and compare to find the minimum and maximum.

Please show all steps for a thumbs up, thank you!

Answer 1