Question

Show all of your work. I should be able to understand your reasoning and how you found your answer. 1. Let f(x,y) = x^2 + y^2 + 8x - 12y + 13 2x + 0 + 8(1) + 0 + 0 a. Find fx(x,y). (1 points) 2x + 0 + 8(1) + 0 = 2x + 8 b. Find fy(x,y). (1 points) x^2 + y^2 + 8x - 12y + 13 = 2y 0 + 2y + 0 c. Find fxx(x,y). (1 points) d. Find fyy(x,y). (1 points) e. Find fxy(x,y). (1 points) f. Use parts (a) and (b) to find the critical point of f. (4 points) g. Determine whether the critical point is a local maximum, a local minimum, or a saddle point. Use the Second Derivative Test For Functions of Two Variables to find your answer. Show your work. (6 points)

          Show all of your work. I should be able to understand your reasoning and how you found your answer.

1. Let f(x,y) = x^2 + y^2 + 8x - 12y + 13
2x + 0 + 8(1) + 0 + 0
a. Find fx(x,y). (1 points)
2x + 0 + 8(1) + 0
= 2x + 8

b. Find fy(x,y). (1 points)
x^2 + y^2 + 8x - 12y + 13 = 2y
0 + 2y + 0
c. Find fxx(x,y). (1 points)

d. Find fyy(x,y). (1 points)

e. Find fxy(x,y). (1 points)

f. Use parts (a) and (b) to find the critical point of f. (4 points)

g. Determine whether the critical point is a local maximum, a local minimum, or a saddle point. Use the Second Derivative Test For Functions of Two Variables to find your answer. Show your work. (6 points)

Show all of your work. I should be able to understand your reasoning and how you found your answer.

1. Let f(x,y) = x^2 + y^2 + 8x - 12y + 13
2x + 0 + 8(1) + 0 + 0
a. Find fx(x,y). (1 points)
2x + 0 + 8(1) + 0
= 2x + 8

b. Find fy(x,y). (1 points)
x^2 + y^2 + 8x - 12y + 13 = 2y
0 + 2y + 0
c. Find fxx(x,y). (1 points)

d. Find fyy(x,y). (1 points)

e. Find fxy(x,y). (1 points)

f. Use parts (a) and (b) to find the critical point of f. (4 points)

g. Determine whether the critical point is a local maximum, a local minimum, or a saddle point. Use the Second Derivative Test For Functions of Two Variables to find your answer. Show your work. (6 points)

Added by Gregory W.

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