- #1
johnhuntsman
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Homework Statement
Find the critical points of f.
[tex]f(x,y)=2+\sqrt{3(x-1)^2+4(y+1)^2}[/tex]
Homework Equations
For fx(x,y) I get:
[tex]f_x(x,y)=0+\frac{1*6(x-1)}{2\sqrt{3(x-1)^2+4(y+1)^2}}=\frac{3(x-1)}{\sqrt{3(x-1)^2+4(y+1)^2}}[/tex]
For fy(x,y) I get:
[tex]f_y(x,y)=0+\frac{1*8(y+1)}{2\sqrt{3(x-1)^2+4(y+1)^2}}=\frac{4(y+1)}{\sqrt{3(x-1)^2+4(y+1)^2}}[/tex]
The Attempt at a Solution
Solving both of these for x and y when set equal to 0, gets me x = 1 and y = -1. However neither of these functions exist when x and y equal those values. Does the original function still have a critical point at (x,y) = (1,-1)?
Additionally, when I put the function into Wolfram Alpha it says that it has no critical points.
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