# Directional derivatives

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

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#### Solution Preview

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) ...

#### Solution Summary

This shows how to find maximum and minimum values of the directional derivative.

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