A note on the fundamental theorem of calculus (Q793858)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A note on the fundamental theorem of calculus |
scientific article; zbMATH DE number 3857410
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the fundamental theorem of calculus |
scientific article; zbMATH DE number 3857410 |
Statements
A note on the fundamental theorem of calculus (English)
0 references
1981
0 references
The theorem alluded to in the title is the following: Let \(y=f(x)\) be a continuous real-valued function on a closed interval \([a,b].\) If f' exists and \(f'(x)>0\) for all \(x\in(a,b),\) then for all c,d such that \(a<c<d<b, f(c)<f(d).\) The author presents a proof which does not appeal to the mean-value theorem.
0 references
criteria for monotonicity
0 references
intermediate value theorem
0 references
fundamental theorem of calculus
0 references
0.7409266233444214
0 references
0.7389089465141296
0 references
0.7231611013412476
0 references
