The formula of the different quotient comes from the plots of a graph. Since the formula helps us find the slope of a straight line, we use the slope formula; but the different quotient helps you find the slope of any curve or line at any single point. Both the different quotient and the slope formula is simply the change in "y" divided by the change in "x"; but the difference is that the slope formula's "y" is used as the y-axis, while in the different quotient the change of "y" is called f(x). The formula for the different quotient helps us find the derivative. The derivative is the slope of the tangent line to a graph f(x), and is usually denoted f '(x). A tangent line is just a line that touches the graph once. A function can have different derivatives at different values of "x". To solve the different quotient, you first have to find f(x+h), then simplify f(x+h)-f(x), you then divide the result from step 2 by "h" (or multiply the result by 1/h).
Slope Formula
Difference Quotient
Tangent Line
Secant Line
Mrs. Kirch's Unit V SSS Packet
http://0.tqn.com/d/create/1/0/9/p/C/-/slopeformula.jpg
http://www.coastal.edu/mathcenter/HelpPages/Difference%20Quotient/img002.GIF
http://clas.sa.ucsb.edu/staff/lee/Tangent%20and%20Derivative.gif
http://clas.sa.ucsb.edu/staff/lee/Secant%20and%20Tangent%20lines.gif
