Unformatted text preview: maximum value, which is 1, when θ = 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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 Calculus, Derivative, Dot Product, directional derivative gives

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