Solution to Question 12. Homework exercises No. 2, Infi 3, December
2001.

(We may perhaps also give solutions of questions 8 and 10 soon.)

First let me tell you the answer. For the first part the vector
should be      -4i-5j      (or in other words (-4,-5)
(or any other vector parallel to this vector is just as
good.) For the second part the vector should be -4i-5j-41k.
(or you can write (-4,-5,-41).  )
(Again, any other vector parallel to this one is fine too.)

Please try first to do this question by yourself without looking at the
solution. You will learn more that way. Here are the relevant questions that
you should be asking yourself.

What function(s) do I want to use? Are they functions of 2 variables or 3
variables? 

 Consider the following questions for n=2 and also for n=3.

What exactly is the geometrical meaning of the directional derivative of a
function of n variables? Suppose that the function is differentiable. In
what direction is it as big (positive) as possible? In what direction is it
as ``small''(negative) as possible? 

This question is designed to help you REALLY know the answers to these
questions, not just to say the words that you read in a book or heard in
lectures.

I will not give full details of the solution yet. Maybe tomorrow
I may say some more.

Bhatzlakha!

M.C.