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Unformatted text preview: maximum value, which is 1, when = 0, which is to say when u points in the direction of x , and its minimum value of 1 when u points in the opposite direction. This gives us a geometric interpretation of the gradient, which will prove very useful. Remark 3.3.5. The gradient vector f ( x ) points in the direction in which the directional derivative has its highest value, known as the direction of steepest ascent , and its length is the value of the directional derivative in that direction. As an example, consider the function f ( x,y ) = 49 x 2 y 2 at the point x = (4 , 1) ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Derivative

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