# Directional Derivative – Calculate maximum value and minimum value – Exercise 4302

Exercise

Calculate the directional derivative of the function

$$z=x^2-xy+y^2$$

At point (1,1) and in the direction that creates an alpha angle with a positive x-axis.

In what direction does the derivative receive maximum value and in what direction does the derivative receive minimum value?

$$(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$$
$$(-\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}})$$