This applet shows interactively the points in which the [i]Rolle's Theorem[/i] for a real function holds true.[br]Type the [i]function expression[/i] in the [math]f(x) [/math] field, and the interval [i]start [/i]and [i]end points[/i] in the [math]a[/math] and [math] b[/math] fields.[br]Move point [math] c[/math] on the x-axis in order to view the different positions assumed by the tangent line to the function graph.

Verify whether the following functions satisfy the hypothesis of Rolle's Theorem in the given intervals, and hence find the point(s) [math]c [/math] as prescribed by the theorem:[br][br][math]f(x)= 1 + |x|[/math] in [math][-1,1][/math][br][math]f(x)= -x^2-x+2[/math] in [math][-1,0][/math][br][math]f(x)=\sqrt(1-x^2)[/math] in [math] [-1,1][/math]