Find the critical points of the following functions. f(x,\ y)=-4x^{2}+8y^{2}-3

smileycellist2

smileycellist2

Answered question

2021-10-15

Find the critical points of the following functions.
f(x, y)=4x2+8y23

Answer & Explanation

Clelioo

Clelioo

Skilled2021-10-16Added 88 answers

Step 1
To find critical points, first find the partial derivative of function f with respect to x and y respectively.
fx=8x
fy=16y
Wquate it to zero,
8x=0
x=0 And
16y=0
y=0
Hence critical point is (0, 0)
Step 2
Let's use the second derivative test to classify the critical points.
Hence, compute
f×=8
fyy=16
fxy=0
And
D=f×fyy[fxy]2
At critical point (0, 0)
D=(8)(16)(0)2
D=128
D<0
This indicates, point (0,0) is a saddle point.

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