What was the question asking for exactly?
Here's the function
x^2 + 4y^2 - 2x - 16y + 13 = 0
Now time to take the derivative with respect to x, I got
fx = 2x + 0 - 2 - 0
= 2x - 2
Now time to take the derivative with respect to y, I got
fy = 0 + 8y - 0 - 16
= 8y - 16
This is what I got so far and Idk wether I did it right.... is there anything i did wrong?
ProveIt: I think the OP meant to implicitly define a graph in the x-y plane, not a function of two variables.
asilvester635: You have , so the minimum and maximum y values are going to occur when . This is when x=1, and plugging in to the equation gives:
So (1,1) is a minimum and (1,3) is a maximum.
As it turns out, there is a more geometric way to analyze this function. Complete the square in both x and y:
so the graph is an ellipse centered at (1,2), and the minimum and maximum points are (1,1) and (1,3) as before.