Fair enough!

Hence the tangent plane is

Well that was nice! The rest of the question is tricky though!

This is where I start to have trouble.

The answer I have so far is

,

and

.

Where

and

and

are the new x,y and z values respectively.

I've been trying to get

in terms of

and

, but I can't elminate t!

Call the tangent plane

.

Hence

.

This is where I start to get a little confused. I was hoping to set

to 0 since the x-y plane has a gradient of 0. However,

is a constant function so can never equal 0!

The problem here is that I appear to have three variables:

and

. This seems to contradict the fact that this is a double integral.

Is z a variable or a constant? If z is a variable then is

?

I would appreciate on any of the parts to this question.

If you have any ideas or explanations to any parts, feel free to post!!