Thread: Parametrization Plane Problem

Find the maximum height above the -plane of a point on
.

( x , y , z )

I found z to be 4. Again, this is trivial. How can I find x and y for this point? Please help!

Originally Posted by Del

Find the maximum height above the -plane of a point on
.

( x , y , z )

I found z to be 4. Again, this is trivial. How can I find x and y for this point? Please help!

Clearly the maximum height above the xy-plane occurs when t(4 - t) has its maximum value.

Consider the parabola f(t) = t(4 - t). Not hard to see that it has a maximum turning point at t = 2.

So the maximum height is 4 and occurs at the point given by r(2) .....