Difference between revisions of "Slope"
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===Introduction to derivative=== | ===Introduction to derivative=== | ||
| − | If a function has value <math>f(x)</math> at <math>x</math> and <math>f(x+h)</math> at <math>x+h</math> with <math>h>0</math> than the | + | If a function has value <math>f(x)</math> at <math>x</math> and <math>f(x+h)</math> at <math>x+h</math> with <math>h>0</math> than the slope of the line joining <math>(x,f(x))</math> to <math>(x+h,f(x+h))</math> is, |
:<math>\frac{f(x+h)-f(x)}{h}</math>. | :<math>\frac{f(x+h)-f(x)}{h}</math>. | ||
| − | Therefor the | + | Therefor the slope of the line that meet (is tangential to) <math>f(x)</math> at <math>x</math> is the limit as <math>h</math> tends to zero, or, |
:<math>\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},</math> | :<math>\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},</math> | ||
Revision as of 02:11, July 4, 2008
Slope is the steepness of a line. A positive slope rises; a negative slope falls. Another term for slope is gradient.
For a straight line, the slope (m) is constant and represented by the difference in the vertical direction (y) divided by the difference in the horizontal direction (x):
The delta, Δ, represents the difference in values between any two points in the x or y direction for straight line. For a curve, the delta, Δ, represents the difference in values for two points in very close proximity to each other.
For a straight line, another way of representing the slope (m) is as follows:
where the two points are located at (x1, y1) and (x2, y2).
Introduction to derivative
If a function has value 
at 
and 
at 
with 
than the slope of the line joining 
to 
is,
.
Therefor the slope of the line that meet (is tangential to) at is the limit as 
tends to zero, or,
which is denoted 
, which is called the derivative of .
