A critical point of f(x, y) is any point where both partial derivatives vanish. Find all critical points of (a) f(x, y) = x 2 − 3xy + y 2 + 2x + 5 (b) f(x, y) = x 2 − 2xy + y 2 (c) f(x, y) = Ax2 + Bxy + Cy2 + Dx + Ey + F

Step-by-step explanation:

Let us find out partial derivatives

Equate these to 0 and solve

we get

Critical point (0.8,1.2)

b)

So (x=y) is the solution

c)

Equate to 0 and solve

2ABx + B^2y +DB =0

2ABx+4ACy +2AE =0

Similarly for x

4ACX + 2BCy +2CD =0

B^2 x +2BCy+BE=0

abde or 1,2,4, 5 is the answer

step-by-step explanation:

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step-by-step explanation: