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gikiian
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A gradient vector points out of a graph (or a surface in 3D case). Locally, it makes an angle of 90 degrees with the graph at a particular point. Why is that so?
Thanks.
Thanks.
The gradient vector points outward from a graph because it represents the direction of the steepest increase in a function. This means that at any given point on the graph, the gradient vector will point in the direction of the greatest increase in the function's output.
The gradient vector is calculated by taking the partial derivatives of a multivariable function with respect to each of its variables. These partial derivatives are then combined to form a vector that represents the direction and magnitude of the function's steepest increase.
No, the gradient vector does not always point outward. It only points outward when the function is increasing in the direction of the vector. If the function is decreasing in the direction of the vector, then the gradient vector will point inward.
Yes, the gradient vector can point in more than one direction. This can occur when the function has multiple local maximum or minimum points. In these cases, the gradient vector will point in the direction of the steepest increase or decrease at each point.
The gradient vector is used in many real-world applications, particularly in fields such as physics, engineering, and economics. It is used to optimize functions and find the most efficient or optimal solutions. For example, in physics, the gradient vector can be used to determine the path of a moving object in a gravitational field or the direction of the electric field at a particular point.