So first of all,
we need to sort of define what we are talking about.
Since we are going to fit our curves,
our surfaces with a linear objects,
let us as always assume as a two-variable case.
Firstly, what we've known
for a single variable k is that we need to
find the best linear approximation
which is a tangent line.
Then we are going to generalize
it's struggled to tangent plane or
hyper plane for the case
of functions of more than two variables.
So what is a tangent plane?
Well, it's kind of essential that since we
define the tangent line as a limit of all secant,
then we need to define
the tangent plane in the same fashion.
We don't need to define second plane,
which is the plane just which goes through
our defined given chosen point.
Then actually it's not
the best approximation and we're seeking
for the fittest one.
Codes and Charles Darwin here.
So since it's quite easy to define this in this way,
we can proceed as follows.
But as you can understand that's not to
constructive way to define our tangent plane.
So we need to elaborate on this further.