Answer :
Final answer:
The critical points of the function f(x,y) = 4x⁵ y ⁴-9x⁷y² can be found by setting the partial derivatives of the function with respect to x and y equal to zero and solving the resulting system of equations.
Explanation:
To find the critical points of the function f(x,y) = 4x⁵ y ⁴-9x⁷y², we need to find the values of x and y where the partial derivatives of the function with respect to x and y are equal to zero.
First, let's find the partial derivative of f(x,y) with respect to x:
∂f/∂x = 20x⁴ y⁴ - 63x⁶y²
Next, let's find the partial derivative of f(x,y) with respect to y:
∂f/∂y = 16x⁵ y³ - 18x⁷y
Now, we set both partial derivatives equal to zero and solve the resulting system of equations:
20x⁴ y⁴ - 63x⁶y² = 0
16x⁵ y³ - 18x⁷y = 0
By solving these equations, we can find the values of x and y that satisfy both equations. These values will be the critical points of the function.
Learn more about finding critical points of a function here:
https://brainly.com/question/32205040
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Final answer:
The critical points of the function f(x,y) = 4x⁵ y ⁴-9x⁷y² can be found by setting the partial derivatives of the function with respect to x and y equal to zero and solving the resulting system of equations.
Explanation:
To find the critical points of the function f(x,y) = 4x⁵ y ⁴-9x⁷y², we need to find the values of x and y where the partial derivatives of the function with respect to x and y are equal to zero.
First, let's find the partial derivative of f(x,y) with respect to x:
∂f/∂x = 20x⁴ y⁴ - 63x⁶y²
Next, let's find the partial derivative of f(x,y) with respect to y:
∂f/∂y = 16x⁵ y³ - 18x⁷y
Now, we set both partial derivatives equal to zero and solve the resulting system of equations:
20x⁴ y⁴ - 63x⁶y² = 0
16x⁵ y³ - 18x⁷y = 0
By solving these equations, we can find the values of x and y that satisfy both equations. These values will be the critical points of the function.
Learn more about finding critical points of a function here:
https://brainly.com/question/32205040
#SPJ14
