Problem:
Illustrate the Mean Value Theorem for the function

f(x) = x3 - 7 x2 + 6 x - 5

for x in the interval [-2, 7].


Visualization:
Using Maple:

> f:=x->x^3-7*x^2+6*x-5;

> plot(f(x),x=-2..7);

> (f(7)-f(-2))/(7-(-2));

10

> plot({f(x),10*(x+2)+f(-2)},x=-2..7);

> g:=x->D(f)(x);

> fsolve(g(x)=10);

-.2700832253, 4.936749892

> plot({f(x), 10*(x+2)+f(-2), 10*(x+.27008)+f(-.27008), 10*(x-4.93674)+f(4.93674)}, x=-2..7);