Locate the critical point of z = (𝑥-5)2 + (𝑦+8)2
Question
Locate the critical point of z = (𝑥-5)2 + (𝑦+8)2
Solution
To find the critical points of the function z = (x-5)² + (y+8)², we need to take the partial derivatives of the function with respect to x and y, and then set them equal to zero.
- Take the partial derivative with respect to x:
∂z/∂x = 2(x-5)
- Set the partial derivative equal to zero and solve for x:
2(x-5) = 0 x-5 = 0 x = 5
- Take the partial derivative with respect to y:
∂z/∂y = 2(y+8)
- Set the partial derivative equal to zero and solve for y:
2(y+8) = 0 y+8 = 0 y = -8
So, the critical point of the function z = (x-5)² + (y+8)² is at (x, y) = (5, -8).
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