Where is derivative 0

The multiplication of both matrices becomes y hat, which is theoretically supposed to be equal to y. I know that in derivative, we are trying to find the rate of change.

The convex combination of minimizers is also in the set of minimizers which proves the minimizers are a convex set. There are a few things that could happen. Either the function has a local maximum, minimum, or saddle point. To determine which one, you need to find out what happens around the point. You can see this by looking at the derivative to the left and right. If there is a sign change, it's an extremum.

If there's no sign change, it's a saddle point. I'll leave it to you to figure out which sign change means maximum or minimum. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Derivative to Zero, What does it intuitively mean?

Outside of astronomy most physical phenomena are not smooth, gradually changing, and orderly. Many objects have fractal structure and their changes can be sudden, explosive and turbulent. Functions describing such phenomena simply do not have derivatives. But exact models of physical events are not always better, because in order to derive conclusions from a model we need adequate mathematical tools. Differential calculus provides such tools for functions having derivatives, but we do not have anything as powerful for more general classes of functions for example, for arbitrary continuous functions.

But there is one mathematical theorem that justifies the use of calculus for phenomena that cannot be described by functions having derivatives. Every continuous function can be approximated with any required accuracy by a function which has a derivative. Thus in practice we use calculus as a mathematical modeling tool for physical phenomena, not because it provides the best descriptions, but because its descriptions are most useful.

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