Section Summary: 3.1

  1. Definitions

    derivative of a function f at a - denoted by tex2html_wrap_inline122 ,

    displaymath116

    provided the limit exists (that's right - this is exactly the same as the slope of the tangent line from section 2.6!). So the derivative of a function f at a point a is the slope of the tangent line to the curve at P(a,f(a)).

    Alternatively, it can be considered the instantaneous rate of change of y=f(x) with respect to x when x=a.

  2. Theorems

    None appeared to my eyes.

  3. Properties/Tricks/Hints/Etc.

    Sometimes the derivative is merely estimated from data, using average rates of change, or by a visual approximation based on a graph.

  4. Summary

    This section is an easy extension of section 2.6: the big picture is that the dreaded derivative, one of the fundamental concepts of calculus, is actually just the same as the slope of a tangent line to a curve. It can also be considered an instantaneous rate of change.

Problems:

pp. 134-135, #1, 2, 6, 8, 16, 20, 25, 32, 34; Board: 5, 8, 16, 25, 32, 33





LONG ANDREW E
Mon Jan 22 23:28:20 EST 2001