Let (x y^2) - (x^3 y)=6 and m = ((3x^2 y)-(y^2)) / ((2xy)-(x^3)). Find all points (x,y) on the curve where the slope is of the tangent line is horizontal, then vertical?

Question

anonymous · Answer

is that m = dy/dx ?

anonymous · Answer

they already gave you the derivative or is that your calculated derivative?

anonymous · Answer

this is the problem I was given. I'm beyond confused

anonymous · Answer

but is that m = dy/dx?

anonymous · Answer

I believe so

anonymous · Answer

ok...let's compute where the tangent is horizontal..

anonymous · Answer

THANK YOU!

anonymous · Answer

what would the slope be if the line is horizontal?

anonymous · Answer

is it 0?

anonymous · Answer

what's the slope of a horizontal line?

anonymous · Answer

yes... zero...

anonymous · Answer

okay so (0, something

anonymous · Answer

right... just set m=0 and you'll be solving this equation:
$$\huge 0=\frac{3x^2y-y^2}{2xy-x^3} $$

anonymous · Answer

so essentially only the numerator will make this equation true so you're actually solving this:
$$\huge 0=3x^2y-y^2 $$

anonymous · Answer

Okay....what exactly am I solving for? I'm sorry I'm having such a hard time. I've been working on 204 calculus/pre-calculus review problems. My brain is fried and I don't remember quite a few things.

anonymous · Answer

|dw:1340928143374:dw|