Find the critical points of the following multivariable function, and using the Second Derivative Test to find the maxima and minima of the equation below: a(x,y)=(8x-y)/(e^(x^2+y^2)

Albarellak 2021-02-19 Answered
Find the critical points of the following multivariable function, and using the Second Derivative Test to find the maxima and minima of the equation below: a(x,y)=8xyex2+y2
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Expert Answer

hajavaF
Answered 2021-02-20 Author has 90 answers

Differentiating the function,
a=8xex2+y2yex2+y2
ax=8[ex2+y21xex2+y22x](ex2+y2)2
ax=8[12x2]ex2+y2
ay=[ex2+y21yex2+y2yx](ex2+y2)2
ay=[12y2]ex2+y2
For critical points, ax=0,ay=0
ax=8[12x2](ex2+y2)2=0
12x2=0
2x2=1
x=±12
ay=[12y2](ex2+y2)2=0
12y62=0
2y2=1
y=±12
The critical points are (±12,±12)
ax=8(12x2)ex2+y2
a×=8(6x+4x3)ex2+y2
ay=(12y2)ex2+y

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