Question

Suppose (a, b) is a critical point for $f(x, y)$. If $f_{xx}(a, b)f_{yy}(a, b) - (f_{xy}(a, b))^2 > 0$ and $f_{xx}(a, b) > 0$, then (a,b) is a ... local minimum local maximum saddle point ... no conclusion can be made about this critical point.

Name: suppose a b is a critical point for fx y if fxxa bfyya b fxya b2 0 and fxxa b 0 then ab is a local minimum local maximum saddle point no conclusion can be made about this critical point 56165
Uploaded: 2022-12-26T02:40:08-08:00
Duration: 2 min 31 s
Channel: Madhur L
Description: suppose a b is a critical point for fx y if fxxa bfyya b fxya b2 0 and fxxa b 0 then ab is a local minimum local maximum saddle point no conclusion can be made about this critical point 56165

          Suppose (a, b) is a critical point for $f(x, y)$.
If $f_{xx}(a, b)f_{yy}(a, b) - (f_{xy}(a, b))^2 > 0$ and $f_{xx}(a, b) > 0$, then (a,b) is a ...
local minimum
local maximum
saddle point
... no conclusion can be made about this critical point.

suppose a b is a critical point for fx y if fxxa bfyya b fxya b2 0 and fxxa b 0 then ab is a local minimum local maximum saddle point no conclusion can be made about this critical point 56165

Added by Teresa C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

12/26/2022

Step 1

Step 1: The given conditions are: $f_{xx}(a, b)f_{yy}(a, b) - (f_{xy}(a, b))^2 > 0$ $f_{xx}(a, b) > 0$ These are the conditions for the second derivative test for a function of two variables. Show more…

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Suppose (a, b) is a critical point for $f(x, y)$. If $f_{xx}(a, b)f_{yy}(a, b) - (f_{xy}(a, b))^2 > 0$ and $f_{xx}(a, b) > 0$, then (a,b) is a ... local minimum local maximum saddle point ... no conclusion can be made about this critical point.