Thread: implicit differentiation (horizontal tangent line)

Given the curve

a) Find



Taking the derivative of the above equation and using product rule for xy, i get,




Answer:


b) Find all points on the curve at which the tangent line is horizontal


Is a) correct? and also how do i do letter b)? i have no clue what to do. thanks!

To find the points that are horizontally tangent find y' of 0.


0=(-2x-y)/(x+2y)

Because the slope will be zero when it is horizontally tangent.

Hope it helps.

oh okay, but im still totally lost, what do i do after that?

Solve you x and y and plug them into point slope form.