Help with partial derivatives

**pakman** · January 14th 2007, 05:55 PM

This is the problem:

Find the slope of the tangent to the curve of intersection of the cylinder 4z = 5*sqrt(16 - x^2) and the plane y = 3 at the point (2, 3, 5*sqrt(3)/2).

I figured I would find d/dx of fx and plug in 2. I got it down to -5x / 2*sqrt(16 - x^2) in which then I plugged in 2 and got -5/12. I'm not sure where to go from here. Any help would be appreciated, thanks.

**ThePerfectHacker** · January 14th 2007, 07:29 PM

Originally Posted by pakman

This is the problem:

Find the slope of the tangent to the curve of intersection of the cylinder 4z = 5*sqrt(16 - x^2) and the plane y = 3 at the point (2, 3, 5*sqrt(3)/2).

I figured I would find d/dx of fx and plug in 2. I got it down to -5x / 2*sqrt(16 - x^2) in which then I plugged in 2 and got -5/12. I'm not sure where to go from here. Any help would be appreciated, thanks.

The cylinder is,
$4z=5\sqrt{16-x^2}$
The plane is,
$y=3$ .

The idea here is to parameterize the curve.
Let $x=t$ .
Then,
$z=\frac{5}{4}\sqrt{16-x^2}=\frac{5}{4}\sqrt{16-t^2}$ .
And $y$ is fixed at $y=3$ .

Thus, the parametric equation for the curve is,
$\left\{ \begin{array}{c} x=t\\ y=3 \\z=(5/4)\sqrt{16-t^2} \end{array} \right\}$

And a point is given $(2,3,5\sqrt{3}/2)$ . That happens when $t=2$ .

Thus, you need to find the derivatives of each parameter evaluated at $t=2$ . That will give thou the tangent vector.

**pakman** · January 14th 2007, 07:41 PM

Thanks for your help! I am still a bit confused though. You say to find the derivatives of each parameter at t=2, but I don't see how I'd take the derivative with respect to y or z. The only one I see is for t... or x... which would be what I posted earlier right?

**galactus** · January 15th 2007, 11:40 AM

I love that signature, PH. May I be one of your marshalls/enforcers when this New World Order arrives?.

**topsquark** · January 15th 2007, 01:21 PM

Originally Posted by galactus

I love that signature, PH. May I be one of your marshalls/enforcers when this New World Order arrives?.

"6.5 billion is not enough, I need more! I need 10 billion. I shall wait for there to be 10 billion and then I shall rule over them. Everyone shall be my slave and bow before my will, my slaves shall hail "Ah! Master". As many slaves as hairs for all hairs on my head I shall have. And my hand and my word shall be feared henceforth. I am the divinity that shapes thou all, rough-hew me who you shall."

Except that by the time we have 10 billion people on Earth he probably won't HAVE any hair...

-Dan

**ThePerfectHacker** · January 15th 2007, 01:36 PM

Originally Posted by topsquark

Except that by the time we have 10 billion people on Earth he probably won't HAVE any hair...

You forget that I am immortal. This is why I seem very young.

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