Maximum directional derivative

Goal: Find a maximum directional derivative 

To find a maximum directional derivative, we use one of the properties of the gradient. This property states as follows:

Other properties of the gradient

1) 

2) 

Example

Find the direction for which the directional derivative of f(x,y) = 3x² - 4xy + 2y² at (-2, 3) is a maximum, What is the maximum value?

Solution

Practice

Find the direction for which the directional derivative of f(x,y) = 4x - xy + 2y² is a maximum at (-2,3). What is the maximum value?