Hi! How can I solve this problem?
- Find the points of the cylinder x=4-z^2 so that the tangent plane is paralell to the plane yz.

Question

Hi! How can I solve this problem? 
- Find the points of the cylinder x=4-z^2 so that the tangent plane is paralell to the plane yz.

anonymous · Answer

Here you can find similar problems: http://www.math.psu.edu/adler/courses/math230/HWs/15_6_hw_soln.pdf

anonymous · Answer

Just perfect! Thank you very much!

anonymous · Answer

you welcome, hope it hepls!!

anonymous · Answer

First of all, this "cylinder" is not a circular cylinder like we're used to from pre-calc, but rather, a similar shape formed from a parabola projected along the y-axis. That is, it doesn't matter what y is; the shape will be the same for all y (or, at any y it will be the same as at any other y-value).

anonymous · Answer

This means that, in effect, the shape (or rather, the surface) is formed by lines parallel to the y-axis|dw:1350320098224:dw|