According to wikipedia:

In mathematics, the gradient is a multi-variable generalization of the derivative. Like the derivative, the gradient represents the slope of the tangent of the graph of the function. More precisely, the gradient points in the direction of the greatest rate of increase of the function, and its magnitude is the slope of the graph in that direction.

If I understand it correctly, this means that the gradient points into the direction of the function to increase the fastest.

But derivative can also be negative, which means that the function is decreasing. So, if gradient and derivative are equal, is the wikipedia statement about "direction of the greatest rate of increase of the function" is wrong, because it can also point to the greatest rate of decrease actually=


closed as off-topic by whuber Feb 16 at 22:32

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  • $\begingroup$ Your quotation refers to a "multi-variable generalization." Thus, you are asking about the gradient as a kind of vector. In what sense can a vector can be "negative" or "positive"? $\endgroup$ – whuber Feb 16 at 22:33
  • $\begingroup$ I see what you mean but why then the gradient points into the direction of the greatest "increase" and not greatest "decrease" ? $\endgroup$ – Alina Feb 16 at 22:39
  • $\begingroup$ Review the definition. (There are many, so use whichever one you prefer.) $\endgroup$ – whuber Feb 16 at 22:41

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