Thread: Implicit differentiation

I was wondering if someone could help me out.
I was given the function f(x,y)=squareroot(1+ x^2 + y^2) and asked to find the slope of a tangent to a level curve at point (-2,2).

I have managed to work out the gradient of f at (-2,2) to be (-2/3, 2/3), and I know it has to be orthogonal to the tangent, but I am unsure as to how to work out the slope of the tangent.

Would appreciate your help

Originally Posted by Pandora

I was wondering if someone could help me out.
I was given the function f(x,y)=squareroot(1+ x^2 + y^2) and asked to find the slope of a tangent to a level curve at point (-2,2).

I have managed to work out the gradient of f at (-2,2) to be (-2/3, 2/3), and I know it has to be orthogonal to the tangent, but I am unsure as to how to work out the slope of the tangent.

Would appreciate your help

Thank you. Would you mind working it out from the facts? I am pretty horrible at implicit differentiation.

Originally Posted by Pandora

Thank you. Would you mind working it out from the facts? I am pretty horrible at implicit differentiation.

Now simplify and solve.