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# Assignment on Average and Instantaneous Rates of Change

by

## Hebe Hou

on 15 October 2012

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#### Transcript of Assignment on Average and Instantaneous Rates of Change

Let's play on a swing!!!!!!!!!!! Average Rate of Change and
Instantaneous Rates of Change The average rate of change of a quantity represented by a dependent variable occurs over an interval of the independent variable.
It can be represented graphically using secant lines.

The instantaneous rate of change of a quantity represented by a dependent variable occurs at a single value of the independent variable.
It can be represented graphically using tangent lines. What are ARC and IRC ????? This is a video I used in my analysis, I'm following the kid in yellow shirt. The video I'm analyzing... y = -36.192x^4 + 510.87x³ - 2544.9x² + 5238.3x - 3552.2 Graph and Equation... The END !!! approaching to ... I tried more than three sequences from both sides because I want to find a more accurate pattern for IRC. If we only use one or two sequences, the deviation of pattern for IRC may exist.
We need to find from both sides (left and right) because this can avoid the "corner".
When the x is close to "4", the slope is approaching to 135.708.
x 4¯ slope 135.708
x 4+ slope 135.708 the x-axis represents time in seconds and y-axis represents vertical height in centimeters, the slope is "vertical height/time" which means vertical speed cm/s. sub x=4 into this equation, we can get the answer "135.708", which is IRC !!!!!! Limit- looking for IRC Process... ARC to IRC Analysis - using Logger Pro Conclusion Through my calculations, I found that both sides (from left and right) are approaching to 135.708.

Therefore, at x=4s, the speed is (slope- IRC)=135.708cm/s
Hebe Hou Thank you ~
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