Finding the Gradient of a Difficult Curve: Tips and Hints

[don1231915]

Difficult gradient problem!

Consider the curve with equation x2 + xy + y2 = 3.
(a) Find in terms of k, the gradient of the curve at the point (−1, k).
(b) Given that the tangent to the curve is parallel to the x-axis at this point, find the
value of k.

 

[Dick]

Consider the curve with equation x2 + xy + y2 = 3.
(a) Find in terms of k, the gradient of the curve at the point (−1, k).
(b) Given that the tangent to the curve is parallel to the x-axis at this point, find the
value of k.

I hope you aren't done posting yet. You are going to show an attempt at solving it, right?

 

[don1231915]

I hope you aren't done posting yet. You are going to show an attempt at solving it, right?

yes, I have no idea how to do (a) but for b I tried substituting 1 and solve for y. I don't know if it is right
I am really confused when it asks for the slope

PLease help if you can!

Thank you so much

P.S. You don't have to provide me with a solution, just some hint or help would be more than helpful.

 

[Dick]

yes, I have no idea how to do (a) but for b I tried substituting 1 and solve for y. I don't know if it is right
I am really confused when it asks for the slope

PLease help if you can!

Thank you so much

P.S. You don't have to provide me with a solution, just some hint or help would be more than helpful.

Ok, here's a hint. Try using implicit differentiation to find the gradient dy/dx. You know about that, yes?