Calculus pp 61-93 | Cite as

The Derivative

  • Harley Flanders
Part of the Textbooks in Mathematical Sciences book series (TIMS)


The graph of a linear function
$$ y = F\left( x\right)= ax + b $$
is a straight line. Its slope a equals the rate of change of y relative to x. A unit change in x produces a change a in y:
$$ F\left( {x + 1} \right) - F\left( x \right) = a\left( {x + 1} \right) - ax = a $$
The ratio-the change in F to a change h in x—equals a:
$$ \frac{{F\left( {x + h} \right) - F\left( x \right)}}{h} = \frac{{a\left( {x + h} \right) - a(x)}}{h} = \frac{{ah}}{h} = a $$
We learned all of this in Chapter 1, Section 2.


Base Point Binary Tree Product Rule Chain Rule Trigonometric Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Harley Flanders
    • 1
  1. 1.University of MichiganAnn ArborUSA

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