clear all;
close all;


%% first function f and its derivative f1
figure(1)
clf
f = @(x) 4.77+x.^7-11.9*x.^6+53.59*x.^5-111.19*x.^4+98.08*x.^3-13.96*x.^2-17.96*x;
f1 = @(x) 7*x.^6-71.4*x.^5+267.95*x.^4-444.76*x.^3+294.24*x.^2-27.92*x-17.96;
alpha0 = 3.8;
x = linspace(0,3.8,200);
c1 = 0.1; c2 = 0.9;


%% second function f and its derivative f1
figure(2)
clf
f = @(x) x.^2 - 1.5*x + 0.5 - sin(pi*x)- 0.35*exp(x) + exp(x-2);
f1 = @(x) 2*x - 1.5 - pi*cos(pi*x) - 0.35*exp(x) + exp(x-2);
alpha0 = 3;
x = linspace(0,alpha0,200);
c1 = 0.01; c2 = 0.9;