Fair enough!let S be the graph of over the square , ie. .
a). Find an equation of the tangent plane to S at
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.b). Write down a normal to S at .
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 .c). At which point is the tangent plane parallel to the x-y plane?
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!!