Math 3 Winter 2004

Introduction to Calculus

Class Demo for the Intermediate Value Theorem

January 12, 2004

>	with(plots):

Warning, the name changecoords has been redefined

   Consider any continuous function

>	f := x -> x^3 - 5*x^2 + 10:

    Have a look at its graph

>	plot(f, -2 .. 6);

    Choose any and so that

>	a := -1.5:

>

b := 5.5:

>	fa := f(a);

>	fb := f(b);

    Choose some  c between and

>

c := 15;

    Look at the graph again

>	display(plot(f(x), x = -2..6, thickness=2), plot({fa, fb, [a, y, y=-10..40], [b, y, y=-10..40]}, -2..6, color = blue), plot(c, -2..6, color=green));

>