I want to make two general graphics something like the following.
I want to illustrate the approach to the function by means of a polynomial. I have tried the following.
Plot[{Sin[x] + 2, Sin[2 x] + 2}, {x, 0, 8}, AxesLabel -> {x, y},
Ticks -> {{0.8, 2.4, 4, 5.5, 7.1}, {0, 1, 2, 3}}]
I also want to put $ x_{0}, x_{1}, x_{2},...,x_{n} $ in the points where the graphs differ the most. I appreciate any help.