Timeline for The role of the mean value theorem (MVT) in first-year calculus
Current License: CC BY-SA 2.5
7 events
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| Jul 13, 2010 at 22:28 | history | edited | Jeff Strom | CC BY-SA 2.5 |
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| Jul 13, 2010 at 14:41 | comment | added | Jeff Strom | Usually on the first day or so of class, I hand out graphs and ask them to draw tangent lines with rulers, then compute slopes and graph the results. The definition is: line up the ruler with the graph. | |
| Jul 12, 2010 at 4:53 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jul 12, 2010 at 1:54 | comment | added | O.R. | You said the first is to draw the tangent and measure its slope. How are you defining tangent there if not with the derivative and the limit that defines it? I think the definition of tangent (its slope) is the derivative. The actual content of the MVT is a continuity argument. Similar to an intermediate value theorem, Rolle, Bolzano, ... Incidentally it relates two values of the function and the value of the derivative at an uncertain point. The main applications are therefore, existence of solutions (of equations) or to pass info from derivative to function and vice versa. | |
| Jul 12, 2010 at 1:44 | comment | added | O.R. | I don't understand why do you need MVT to do anything about tangents. Am I calling MVT something different? Slope of tangents as limiting position of cords is exactly what the definition of derivative (with the limit) says. No even need of continuity and therefore of MVT. Think about it, you can define tangent and slope on the rational numbers. | |
| Jul 11, 2010 at 23:16 | comment | added | Pete L. Clark | +1. $ $ | |
| Jul 11, 2010 at 23:05 | history | answered | Jeff Strom | CC BY-SA 2.5 |