How to I find the intersection point between y=x*exp(x)/(exp(x)-1) and y=3? I can't seem to have the intersection point displayed.

x = 1:1:10;

f = @(x) x.*exp(x);

g = @(x) exp(x)-1;

y_1 = @(x) f(x)./g(x);

y_2 = @(x) yline(3,'b');

intersection = find(y_1(x)==y_2(x));

x_intersection = x(intersection);

y_intersection = y_1(intersection);

plot(x,y_1(x),'red')

hold on

plot(x,y_2(x),'blue')

intersection = plot(x_intersection,y_intersection,'Marker','+','Color''g')

Answer 1

[Simon Chan]

Use function fzero to help you to find the intersection.

x = 1:1:10;
f = @(x) x.*exp(x);
g = @(x) exp(x)-1;
y_1 = @(x) f(x)./g(x);
y_2 = @(x) yline(3,'b');
y_intersect = 3;
x_intersect = fzero(@(x)y_1(x)-y_intersect, 10);
plot(x,y_1(x),'red')
hold on
plot(x,y_2(x),'blue')
intersection = plot(x_intersect,y_intersect,'g+');

[Craig Egan Allistair Tan]

Thanks!