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)); |
> |