Author: Benny Varghese

a bentech presentation.....
Verification of Rolle's theorem

Drag the slider above to get various tangents....
and observe that at x =1.5 the tangent is
parallel to the x axis

x_2 = 5
x_1 = -2
f(x) = x^(2.0) - 3.0 * x + 2.0
f_r = Function(f, x_1, x_2)
B = Point(f_r)
f_1(x) = f'(x)
f_2(x) = f''(x)
a = 2.8 (slider from -2 to 5, step 0.1)
T_f(x) = f'(a) * (x - a) + f(a)
C = Intersect(f_r, T_f)
A = Point(f_r)
T1: "f'(x) \, = \, " + f_1
T2: "f'(a) \, = \, " + (f_1(a)) + "\,\, \fgcolor{0000FF}{(slope \,\, of \,\, T_f)}"
T3: "\fgcolor{FF0000}{f(x) \, = \, " + f + "}\,\, on \,\, interval\,\,\fgcolor{640064}{[ " + x_1 + "," + x_2 + "]}"
D: (x_1, f(x_1))
E: (x_2, f(x_2))