Difference between revisions of "Math 22 Rates of Change"
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| − | ==Average Rate of Change=== | + | ==Average Rate of Change and velocity== |
| + | If <math>y=f(x)</math>, then the average rate of change of <math>y</math> with respect to | ||
| + | <math>x</math> on the interval <math>[a,b]</math> is <math>\frac{f(b)-f(a)}{b-a}=\frac{\Delta y}{\Delta x}</math> | ||
| + | ==Instantaneous Rate of Change and Velocity== | ||
| + | The instantaneous rate of change of <math>y=f(x)</math> at <math>x</math> on the interval <math> | ||
| + | [a,b]</math> is | ||
| + | <math>\lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}</math> for <math>\Delta x =b-a</math> | ||
| + | |||
| + | ==Notes== | ||
| + | 1) If <math>p=f(x)</math> is the demand function, then Revenue function will be <math>R(x)=x.p=x.f(x)</math> | ||
| + | |||
| + | 2) The profit function <math>P(x)</math> can be calculate as <math>P(x)=R(x)-C(x)</math> where <math>R(x)</math> is revenue function and <math>C(x)</math> is the cost function. | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 07:48, 19 July 2020
Average Rate of Change and velocity
If , then the average rate of change of with respect to on the interval is
![{\displaystyle [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935)
Instantaneous Rate of Change and Velocity
The instantaneous rate of change of at on the interval is for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta x =b-a}
Notes
1) If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p=f(x)} is the demand function, then Revenue function will be Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R(x)=x.p=x.f(x)}
2) The profit function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P(x)} can be calculate as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P(x)=R(x)-C(x)} where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R(x)} is revenue function and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C(x)} is the cost function.
This page were made by Tri Phan