To find critical points, you need to use this formula
This is driving me nuts... I've put in a good few hours and still stuck.. can't seem to find much on this online either.
OK, I'm trying to draw the curve of
I used implicit differentiation to find
I put this equal to zero to find critical points.. gives me
I plug this back into the original equation to simplify to
so I have .
And I'm stuck (badly)
I need to find the turning points and to draw the curve.. Any help?
Plugging them into will give you the coordinates zero gives
Now if you set the denominator equal to zero you will get the coordinates of the vertical tangents.
putting these back into the original gives
Now putting these into
From here pick a few x values to so how the graph is behaving away from the loop.
for example and and solve for y to get some ordered pairs. Also once you have a few ordered pairs to can evaluate the derivative to get an idea of how fast the graph is changing at that point.
P.S the graph should look like this.