3.1 Derivatives of Polynomials and Exponentials

Mathematica script by Chris Parrish,
   cparrish@sewanee.edu

Problems from James Stewart,
  "Calculus," Second Edition, Brooks/Cole, 2001

A Polynomial and Its Derivative.

Stewart, section 2.10, Example 1, page 175

Let's plot a cubic polynomial, and its first derivative.
Your task is to relate the "behaviours" illustrated by these two graphs.
What sort of correspondences do you see?

<<Graphics`Colors`

Clear[f, x]  f[x_] := x (x - 1) (x + 1)  Plot[{f[x], f '[x]}, {x, -2, 2}, > ... p;       PlotStyle  {MediumTurquoise, PrussianBlue}] ;

[Graphics:HTMLFiles/3.1_derPolyExp_3.gif]

Derivatives of Some Exponential Functions.

Stewart, section 2.10, Example 1, page 175

Let's plot several exponential functions
Focus on the slopes of their tangent lines at the point P(0,1). Stretch out the graph for a better view.

In[13]:=

Clear[f, g, h, x]  f[x_] := 3^x ; g[x_] := Exp[x] ; h[x_] := 2^x ;  tanF[x_] : ... sp;         MediumTurquoise, CobaltGreen, Orchid}] ;

[Graphics:HTMLFiles/3.1_derPolyExp_5.gif]


Created by Mathematica  (April 19, 2004)