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### Reason for relaxing limit in derivative in this context?

The equation $$f(x + \epsilon) \approx f(x) + \epsilon f'(x)$$ is justified from taylor series. It is not derived from the limit definition of a derivative. Let $f'(a)$ and $f''(a)$ exist for $a$ in ...
• 931
1 vote

### Why does critical points and stationary points are used interchangeably?

From reading the text, it's clear that the authors are using critical point to mean the same thing as stationary point, so they are not using the proper mathematical definition. More generally, ...
• 931
1 vote

### Why does critical points and stationary points are used interchangeably?

A critical point of a function $f$ can be a stationary point (i.e. $f'(x) = 0$), or a point where the derivative is undefined (for example, in the case of the absolute value function $f(x)$, $x=0$ is ...
• 34.4k
1 vote

### Reason for relaxing limit in derivative in this context?

It is just an assumption. If we assume $\epsilon$ is small enough (depending on the function $f$), you can remove the limit $\lim_{\epsilon \to 0}$ for the approximation.
• 1,663
1 vote

### Why is my derivation of the back-propagation equations inconsistent with Andrew Ng's slides from Coursera?

TL;DR: This has to do with the way A. Ng has defined back propagation for the course. Left Column This is only with respect to one input example and so the $\frac{1}{m}$ factor reduces to 1 and can ...
• 1,016

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