Author Topic: Implicit Differentiation - HELP PLEASE (Read 1039 times) Tweet Share

Electroflame1395 · « **on:** May 30, 2013, 06:04:50 pm »

Hey, I'm stuck with one question on implicit differentiation.

Find the equation of the tangent parallel to the x-axis for: x^2-2xy+2y^2=4.
I managed to differentiate the equation and i got it to be: dy/dx = (x-y)/(x-2y)
I don't know what to do next but I am think since the tangent equation is parallel ti the x-axis the gradient has to be 0. Therefore make dy/dx = 0.

Please if anyone can help is would be great.
Thanks

BubbleWrapMan · « **Reply #1 on:** May 30, 2013, 06:19:55 pm »

$\frac{\mathrm{d}y}{\mathrm{d}x}=0$ when $y=x$ , so replace $x$ with $y$ in the original formula for the curve and solve for $y$ . This will give you the horizontal tangents.

b^3 · « **Reply #2 on:** May 30, 2013, 06:30:56 pm »

Well since the gradient is zero, $\frac{dy}{dx}=0$ , as you have said. So what do we find out?
$\begin{alignedat}{1}\frac{x-y}{x-2y} & =0 \\ x-y & =0 \\ \implies x & =y \end{alignedat} $

That is the only time that our gradient will be zero, is when $x$ and $y$ are equal. So if we substitute that back into our original equation, then we should be able to solve for $y$ , we will get the $y$ value of the points for which the gradient is zero. As the gradient is zero, the line will be given by $y=_$ .

Spoiler

$\begin{alignedat}{1}\left(y\right)^{2}-2\left(y\right)y+2y^{2} & =4 \\ y^{2}-2y^{2}+2y^{2} & =4 \\ y^{2} & =4 \\ y & =\pm\sqrt{4} \\ y & =\pm2 \end{alignedat} $

Hence the equation for the tangents are $y=-2$ and $y=$

EDIT: Beaten.

Electroflame1395 · « **Reply #3 on:** May 30, 2013, 06:41:02 pm »

thanks guys i knew i was on the right track but just wasn't able to finish it off.

Search the forums now!

We have moved!

Author Topic: Implicit Differentiation - HELP PLEASE (Read 1039 times) Tweet Share

Electroflame1395

Implicit Differentiation - HELP PLEASE

BubbleWrapMan

Re: Implicit Differentiation - HELP PLEASE

b^3

Re: Implicit Differentiation - HELP PLEASE

Electroflame1395

Re: Implicit Differentiation - HELP PLEASE

Recent Posts

User:
Password: