Consider the function :
f(x,y) = x(x-1)(x-2) + (y-1)(x-y)
[QUESTION 1]find the maximum and the minim values of the
directional derivative (df/ds)]u at ( 1 , 3/2 ) as u varies .
( (df/fs)]u : I can't write the symbol clearly but it means : the derivative of f according to s on the direction of u (u is a unit vector).
[QUESTION 2] In which direction(s) "u", the maximum and the minimum occur?.
[QUESTION 3] What are the directions "u" for which (df/ds)u]=0
In x direction, df/dx=(x-1)(x-2)+x(x-2)+x(x-1)+(y-1)
In y direction, df/dy=(x-y)-(y-1)
at the point (1,3/2) ...
This shows how to find maximum and minimum values of the directional derivative.