% question3.m
% Find first three positive roots of
% the function f(x) = tanh(x) + tan(x)

% First define data for the plots

x = linspace(0,12,100); % 100 points between 0 and 12
y1 = tanh(x);
y2 = -tan(x);

% plot intersections in window with
% 0 <= x <= 12, and -2 <= y <= 2

plot(x,y1,'-', x,y2,'--');

axis([0,12,-2,2]); % note the square brackets

% Estimate intervals on which the following
% function f changes sign and find first 3 roots using fzero

f = @(x) tanh(x) + tan(x);
format long

r1 = fzero(f, [2,3])
r2 = fzero(f, [5,6])
r3 = fzero(f, [8,10])

%r1 = fzero(f, 3)
%r2 = fzero(f, 6)
%r3 = fzero(f, 9)

sr1 = secant(f, 2, 3, 0.5E-5, 10, true)
sr2 = secant(f, 5, 6, 0.5E-5, 10, true)
sr3 = secant(f, 8, 10, 0.5E-5, 10, true)