Proving Third Order Accuracy of R-K Method for x'=x, x(0)=1

[Jopi]

Homework Statement

$$x'=f(t,x)$$
$$k_1=f(t_n,x_n)$$
$$k_2=f(t_n+2h/3,x_n+2h k_1/3)$$
$$k_3=f(t_n+2h/3,x_n+h(k_1+3k_2)/6$$
$$x_{n+1}=x_n + h(k_1+ k_2+2k_3)/4$$

Prove that the above Runge-Kutta method is of third order by examining the problem
$$x'=x, \; x(0)=1$$.

Homework Equations

The Attempt at a Solution

I have to prove that the difference between the exact solution (which is exp(x)) and the solution given by the RK is of magnitude h⁴, where h is the step size. I'm just being very thick-skulled here, I can program this in Matlab but I can't do it on paper.
Can someone just show me how I calculate k₁, k₂ and k₃? I don't completely understand the notation used. What is f(t_n,x_n)?

 

[Nino MMP]

My understanding is that I have to plug the stuff in the equation but I can't figure out what the values are.