Help with finiding coords when dy/dx =0

The curve C has equation 16y^3 +9x^2 y - 54x=0

I need to find the coords of the points on C where dy÷dx= 0

Using implicit differentiation i worked out dy/dx to be = (54-18xy)/ (48y^2 +9x^2)

How do you work out the coords for this if we have two unknown variables in the equation? Do you take simultaneous equations? I even tried mmaking x and y 0 to work out the other but that doesnt work. Can you explain please?

The curve C has equation 16y^3 +9x^2 y - 54x=0

I need to find the coords of the points on C where dy÷dx= 0

Using implicit differentiation i worked out dy/dx to be = (54-18xy)/ (48y^2 +9x^2)

How do you work out the coords for this if we have two unknown variables in the equation? Do you take simultaneous equations? I even tried mmaking x and y 0 to work out the other but that doesnt work. Can you explain please?

Remember that there's always $16y^3 + 9x^2 y - 54 x = 0$ lying around and begging to be used. (that wasn't meant to sound dirty).

Remember that there's always $16y^3 + 9x^2 y - 54 x = 0$ lying around and begging to be used. (that wasn't meant to sound dirty).

Well i tried taking all the y figures from the equation that is beggingto be used and divided it by 0 to cancel it out. That gave me a quadratic equation which gives me the answer x=5.68 & x=0.31

Am i on the right track?

Well i tried taking all the y figures from the equation that is beggingto be used and divided it by 0 to cancel it out. That gave me a quadratic equation which gives me the answer x=5.68 & x=0.31

Am i on the right track?

Not at all, you know that $\frac{dy}{dx} = 0 \iff 54 - 18xy = 0$

So now you have two simultaneous equations, $54-18xy = 0$ and $16y^3 + 9x^2y - 54x = 0$

What you've done doesn't seem to get you anyway (dividing by 0 is nasty business )

What do you think about the previous hint that I've given?

Hey Sean Fm your hint got me as far as i got with that girl at the pub after i bought her a pint of beer and 2 min later she decided to leave with her friends.

But thats only cause im really stupid and didnt know what you meant by the denominator "trick"

Thanks Zacken saved my ass again. Ill try to work this out abd keep it in my head. I knew when you have two unkown variables you can use simultaneous equations but didnt know exactly how to set it up.

nice analogy.

If $\frac{a}{b} = 0$ then the only way for that to be 0 is for a=0. There is no value of b for which a/b = 0 .

Glad it helped.



Sorry for butting in, by the way.

Sorry Zacken i feel really stupid. Cant seem to work out the simultaneous equation either. Ive done it on a simple level before but nothing with x^2 y and y^3 and. I need a breakdown about this if possible. Come to the rescue one more time will you?

$54 - 18xy = 0 \Rightarrow x = \frac{54}{18y}$ - simplify that and then substitute it into the other equation to find $y$ and then plug it back into the above to find $x$.