# The function ๐(๐ฅ,๐ฆ)=๐ฅ3โ3๐ฅโ2๐ฅ๐ฆโ๐ฆ2โ2๐ฆ+4 has two critical points. Find and classify them

## Question

## Solution 1

To find the critical points of the function, we first need to find the partial derivatives of the function with respect to x and y.

The partial derivative of f with respect to x is:

f_x = 3x^2 - 3 - 2y

And the partial derivative of f with respect to y is:

f_y = -2x - 2y - 2

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## Similar Questions

The function ๐(๐ฅ,๐ฆ)=๐ฅ3โ3๐ฅโ2๐ฅ๐ฆโ๐ฆ2โ2๐ฆ+4 has two critical points. Find and classify them

If ๐ง=๐ ๐๐โก(3๐ฅ+2๐ฆ), determine 3โ2๐งโ๐ฆ2-2โ2๐งโ๐ฅ2Question 9Answera.-6๐ ๐๐โก(3๐ฅ+2๐ฆ)b.12๐ ๐๐โก(3๐ฅ+2๐ฆ)c.6๐งd.6๐๐๐ โก(3๐ฅ+2๐ฆ)

Show that the following system of equations has unique solutions. Find its solution by thereduction method๐ฅ + ๐ฆ + ๐ง = 2, ๐ฅ โ 2๐ฆ + ๐ง = 8, 3๐ฅ + ๐ฆ + ๐ง = 4

If ๐ข = ๐ฅ2 tanโ1 ๐ฆ๐ฅ โ ๐ฆ2 tanโ1 ๐ฅ๐ฆ show that ๐2๐ข๐๐ฅ๐๐ฆ = ๐ฅ2โ๐ฆ2๐ฅ2+๐ฆ2 and ๐2๐ข๐๐ฅ๐๐ฆ = ๐2๐ข๐๐ฆ๐๐ฅ.

Given the following system of equations:3๐ฅโ2๐ฆ=73xโ2y=7๐ฅ+๐ฆ=โ1x+y=โ1Solve to find the solution to the system.

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