Evaluate the stationary points of the function f(x,y)=xy left x{2}+y{2}-1 right
i really need to see how to solve this math plsss
Is that supposed to be f(x,y) = xy(x^2 + y^2 - 1) ?
To find the stationary points of the function f(x, y) = xy, you need to find the critical points where the gradient is equal to zero or does not exist.
Step 1: Calculate the partial derivatives of f(x, y) with respect to x and y.
∂f/∂x = y
∂f/∂y = x
Step 2: Set the partial derivatives equal to zero and solve for x and y simultaneously.
y = 0
x = 0
Step 3: Substitute the values of x and y back into the original function to obtain the coordinates of the stationary points.
f(0, 0) = 0*0 = 0
So, the only stationary point of the function f(x, y) = xy is (0, 0).