Slope

[TheNextOne]

Find all points (x, y) on the curve x2 +xy +y2 = 9 for which the slope of
the tangent to each such point is equal to 1.

How would i do this? Should i use implicit differentiation?

 

[skeeter]

yes

once you find the derivative implicitly in terms of x and y, set that equal to 1, then solve for either x or y and substitute into the original equation to get it in terms of a single variable ... solve for that variable and finally, determine the value of the other variable.

you should get two points on the curve where the slope = 1.

 

[tkhunny]

It wouldn't hurt to know what you are dealing with. How many solutions are you expecting?