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anonymous
 5 years ago
local extremes values of ; ln (x ^ 2 + y ^ 2 +1)
anonymous
 5 years ago
local extremes values of ; ln (x ^ 2 + y ^ 2 +1)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Find derivative respect to x Find derivative respect to y

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f[x,y]\text{=}\text{Log}\left[1+x^2+y^2\right]\] Derivative of f[x,y] with respect to x: \[\frac{2 x}{1+x^2+y^2} \] The same with respect to y: \[\frac{2 y}{1+x^2+y^2} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Not exactly same, one is 2x, one is 2y. Set each to zero and solve for x and y (simultaneous equations). Solution x,y is critical point.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0By inspection, both x and y are equal to zero and the point looks "extreme" in the everyday sense. Refer to the 3D plot. Check the coordinates. The plot may be upside down because it looks better that way.
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