Código da parte 1 vFinal

syms x T;
assume (x ~= -1);

figure(1)
title("Função")
axis([-5 4 -10 50])
fplot(f(x))

figure(2)
title("É par ou ímpar")
axis([-5 4 -10 50])
hold on
par = logical(f(x) == f(-x)) %0 false, 1 true
impar = logical(-f(x) == f(-x)) %0 false, 1 true
fplot(f(x) - f(-x))
fplot(f(x) + f(-x))
fplot(0, 'LineStyle', '- -')
hold off

[periodo, ~, conditions] = solve(f(x + T) - f(x) == 0, x, 'ReturnConditions',true) %if returns with no conditions then

figure(3)
title("Zeros")
hold on
zeros = solve(f(x) == 0)
axis([-1 1 -1 1])
fplot(f(x))
fplot(0)
for zero = zeros
    scatter(zero, 0)
end
hold off
figure(4)
title("Zeros")
hold on
zeros = solve(f(x) == 0)
axis([-5 4 -10 50])
fplot(f(x))
fplot(0)
for zero = zeros
    scatter(zero, 0)
end
hold off

figure(5)
title("Assíntotas")
axis([-20 20 -2 14])
hold on
fplot(f(x))
limiteNaDescontinuidade = limit(f(x), x, -1) %Se +-Inf, ent x = -1 é uma assintota vertical
xline(-1, 'b')
%Assíntotas horizontais e oblíquas
m = limit(f(x)/x, x, inf);
assintota1 = limit(f(x) - m*x, x, inf)
fplot(assintota1)
m = limit(f(x)/x, x, -inf);
assintota2 = limit(f(x) - m*x, x, -inf)
%aqui a assintota1 = assintota2 portanto não é preciso desenhar essa segunda
legend('y = f(x)', 'x = -1', 'y = 2')
hold off

figure(6)
title("Derivadas")
hold on
axis([-5 4 -10 20]);
l = axis;
derivada1 = diff(f(x))
derivada2 = diff(derivada1)
fplot(f(x))
fplot(derivada1, 'r')
fplot(derivada2, 'b')
zerosD1 = solve(derivada1 == 0, x);
for zero = zerosD1
    scatter(zero, 0, 'r')
end
zerosD2 = solve(derivada2 == 0, x);
for zero = zerosD2
    scatter(zero, 0, 'b')
end
fplot(0, 'LineStyle', '- -')
legend('y = f(x)', "y = f'(x)", "y = f''(x)")
ylD2 = l(3)+8;
ylD1 = l(3)+5;
ylD0 = l(3)+2;
ylD0D1 = ylD0+0.5;
ylD0D2 = ylD0-0.5;
text(l(2), ylD2 , "f''");
text(l(2), ylD1, "f'");
text(l(2), ylD0 , "f");
mid = (l(1) + -1)/2;
text(mid, ylD1, '+')
text(mid, ylD0D1, '↗')
text(mid, ylD2, '+')
text(mid, ylD0D2, '◡')
text((-1 + zerosD1)/2, ylD1, '-')
text((-1 + zerosD1)/2, ylD0D1, '↘')
text((-1 + zerosD2)/2, ylD2, "+")
text((-1 + zerosD2)/2, ylD0D2, "◡")
text(zerosD1, ylD1, '0')
text(zerosD1-0.1, ylD0D1, num2str(double(f(zerosD1))))
text((zerosD1 + l(2))/2, ylD1, "+")
text((zerosD1 + l(2))/2, ylD0D1, '↗')
text(zerosD2, ylD2, "0")
text(zerosD2, ylD0D2, num2str(double(f(zerosD2))))
text((zerosD2 + l(2))/2, ylD2, "-")
text((zerosD2 + l(2))/2, ylD0D2, "◠")
hold off
function y = f(x)
    y = (2*(x ^ 2) + x) /((x + 1)^2);
end