increasing/decreasing function?

[apple2357]

Ok, all this is making sense to me now. Thanks.
BTW, this is a photo from the textbook of the Introduction to the topic:



This felt like definitions to me rather than a theorem.

 

[Dr.Peterson]

Yes, that looks like the sort of slightly deficient introduction I expected to find. They have leaped over the actual definition (and even, apparently, an informal description of what "increasing" looks like in a graph) to the calculus-based characterization that results from a theorem.

But I observe that they have not lied! They say that IF the derivative is positive everywhere, THEN the function is increasing. That's true! They didn't say it can't be increasing under other conditions (though it is natural to read this as if it were a definition, identifying all conditions).

 

[Agent Smith]

@apple2357 is the book you're using downloadable anywhere?
@Dr.Peterson , that book you're using to take excerpts from, where can I find it?

Gracias to both.

 

[Dr.Peterson]

@Dr.Peterson , that book you're using to take excerpts from, where can I find it?

I gave the link:

3.3: Increasing and Decreasing Functions

In this section we begin to study how functions behave between special points; we begin studying in more detail the shape of their graphs. The first derivative of a function helps determine when the …

math.libretexts.org

It's an online textbook.

 

[Agent Smith]

@Dr.Peterson much obliged. Gracias, muchas.

 

[apple2357]

@apple2357 is the book you're using downloadable anywhere?
@Dr.Peterson , that book you're using to take excerpts from, where can I find it?

Gracias to both.

My book was a hard copy which i took a photo of. As far as i know it is not available online.