Difference between revisions of "Math 22 Rates of Change"
(Created page with "==Average Rate of Change=== '''This page were made by Tri Phan'''") |
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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 06:48, 19 July 2020
Average Rate of Change and velocity
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 y=f(x)}
, then the average rate of change of 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 y}
with respect to
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 x}
on the interval 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 [a,b]}
is
Instantaneous Rate of Change and Velocity
The instantaneous rate of change of at 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 x}
on the interval 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 [a,b]}
is
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 \lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}}
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