Relative extrema of multivariables: f(x,y)= (xy)/7 find critical points and relative extrema, given an open region.

sibuzwaW 2020-10-27 Answered
Relative extrema of multivariables:
f(x,y)=xy7
find critical points and relative extrema, given an open region.
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Expert Answer

Clara Reese
Answered 2020-10-28 Author has 120 answers

We have, f(x,y)=xy7
To find the critical point:
Find the partial derivative and equate to zero:
Now,
Differntiate f(x,y) with respect to x and equate to zero
fx(x,y)=y7=0
y=0
Differntiate f(x,y) with respect to y and equate to zero
fy(x,y)=x7=0
x=0
Hence, the critical point is (0,0)
Now we have to find the relative extrema.
Use:
D(x,y)=fxx(x,y)fyy(x,y)(fxy(x,y))2
Find D(0,0):
Now
fxx(0,0)=0
fyy(0,0)=0
fxy(0,0)=17
Therefore,
D(0,0)=0×0(17)2=149<0
Hence, by the 2nd derivative test:
f(x,y) neither max. nor min at (0,0) which means (0,0) is saddle point.

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