c.6.htm, T9/23,M9/22, Fall 2025, MAT131 Notes

MAT131 Fall 2025 Notes
mathnstuff.com/math/calc/MAT131fa25/c.6.htm
© 9/24/2025, A², Agnes Azzolino Instantaneous Rates of Change and Interpretations of the Derivative (2.1-2.2, pg. 59 )

$calc.fa25$

Welcome to Calc I!

Hi,: This stuff is REALLY important.; The typical US math curriculum has been presenting work to you
so you would be able to comprehend and master the idea that "A derivative is the
instantaneous rate of change of the difference quotient, the slope, of a function. ": 1st: In the fist sequence of figures below, examine closely from
left to right the use of slope.: 2nd: That mastered, attack the list of other resources listed next.; 3rd: That completed, read the text and do the odd problems.; If needed, contact me through the pink box on; www.mathnstuff.com/math/math.htm; Stay safe, A²

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The difference quotient is really the slope.
For more info see: The Dope on Slope,
Take A Derivative by Taking The Limit of A Difference Quotient.
Use Dynamic Analytic Geometry to Take A Derivative with Limit.gsp.
Print for next class: # 4, Derivatives Connect-the-dots
Be sure you know:
* how to take a derivative by definition
* the difference between average rate of change and instantaneous rate of change.

Some Algebraic Examples Using a Difference Quotient to Take a Derivative
	Derivative Proofs d(e^x)/dx= e^x d( sin(x) )/dx = cos(x) d(polynomial)/dx examples more examples