When we want to find the directional derivative in a particular direction then we take grad(f).u, where u-unit vector in the direction we want to find the rate of change or directional derivative. So from the above equation it means the that grad(f) gives the rate of change at a particular point and grad(f).u this gives the component along u.
Does gradient gives the rate of change for a field in general in space or at a particular point?
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multivariable-calculus
vector-analysis
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0I don't think it's possible to speak of a rate of change of a function without specifying a direction – 2017-01-26
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0The gradient points in the direction of maximum change and its length is the rate of change in that direction. – 2017-01-26