Question

You are give that f (x,y) = x^2+4xy+4y^2+33, fx (x,y)=2x+4y and fy (x,y) = 4x+8y. Which one of the following statements is true?

(a) (2,1) is a critical point of f(x,y)
(b) (0,0), (2,-1) and (-2,1) are the only critical points of f(x,y)
(c) (2b,b) is a critical point of f(x,y) for every real number b.
(d) (2b,-b) is a critical point of f(x,y) for every real number b
(e) f(x,y) has no critical points.

Answer 1

d
All the points on the line (2b,-b) make the gradient of f ZERO

Answer 2

thank you!