# 6.1  Finding Absolute Extremes of a Function on an Interval
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 6.1.
# In-line plots have been removed to conserve disk space.
> restart; f:=ln(x) - 4*x^2 + x^3; plot(f, x=1..3);

                                        2    3
                        f := ln(x) - 4 x  + x

> Df:=diff(f, x); xmin:=fsolve(Df=0, x=2..3);

                                             2
                        Df := 1/x - 8 x + 3 x


                         xmin := 2.618033989

> f:=(x^4 + 2*x + 3) / x^2; plot(f, x=0..20, y=-100..100);

                                4
                               x  + 2 x + 3
                          f := ------------
                                     2
                                    x

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