The [b]INTERMEDIATE VALUE THEOREM [/b]states:[br][br]If g is a CONTINUOUS FUNCTION over [a,b], and if [color=#1e84cc][b][i]N[/i] = any output[/b][/color] between g(a) and g(b), where g(a) and g(b) are not equal, then [color=#980000][b]there exists an input c[/b][/color] in the open interval (a,b) so that [b]g([color=#980000]c[/color]) = [i][color=#1e84cc]N[/color][/i].[/b] [br][br]This applet dynamically illustrates this fact. [br][color=#9900ff][b][i]Just make sure the function you enter is CONTINUOUS over [a,b]! [/i][/b][/color][br][br]Note: [b]You can simply drag points A and B to the left and right to adjust the values of a and b. [/b] [br] [color=#1e84cc][b]You can also simply enter in any [i]N [/i]value between g(a) and g(b) by moving the BIG BLUE [br] POINT or simply by entering in a value. [/b][/color]