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The function ๐‘“(๐‘ฅ,๐‘ฆ)=๐‘ฅ3โˆ’3๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’๐‘ฆ2โˆ’2๐‘ฆ+4 has two critical points. Find and classify them

Question

The function ๐‘“(๐‘ฅ,๐‘ฆ)=๐‘ฅ3โˆ’3๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’๐‘ฆ2โˆ’2๐‘ฆ+4 has two critical points. Find and classify them
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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

Setting these equal Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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The function ๐‘“(๐‘ฅ,๐‘ฆ)=๐‘ฅ3โˆ’3๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’๐‘ฆ2โˆ’2๐‘ฆ+4 has two critical points. Find and classify them

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Given the following system of equations:3๐‘ฅโˆ’2๐‘ฆ=73xโˆ’2y=7๐‘ฅ+๐‘ฆ=โˆ’1x+y=โˆ’1Solve to find the solution to the system.

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