Finding the tangent of two curves

For A Homework Project I have to find the point at which two curves are tangent.

I wrote the following script but it gives me an error:

          Warning: 2 equations in 1 variables.

I do not understand this warning, but my teacher said it should not be there. Here is My Script:

syms x y;

y1 = x^3-3*x+4;
y2 = 3*(x^2-x);

y1_prime = diff(y1);
y2_prime = diff(y2);

possible_xs = solve(y1 == y2, x1_prime == x2_prime);

slope = subs(y1_prime, x, x_point);

y_point = subs(y1, x,x_point);

tangent_line = solve(y - y_point == slope*(x - x_point), y); 

fprintf('The equation for the tangent line is: %s\n', string(tangent_line));

Please Help. Thank You :)

Answer 1

[Walter Roberson]

You have

solve(y1 == y2, x1_prime == x2_prime)

y1 and y2 and x1_prime and x2_prime all only involve a single variable, "x". So you are trying to solve two equations that only have a single variable between them. Much of the time if you have two equations in one variable, there is a contradiction between the two equations and there ends up being no solution. So usually having two equations in one variable represents a logic error, so MATLAB gives you a warning about the situation.

Hint: if you were doing a Venn diagram of solutions of the equations, what would the overlap be called?