Here we are tasked with comparing our calculated solution from Problem 1 against the correct solution \( y(x) = (\frac{f}{24EI})x^2(x^2-4Lx+6L^2) \). We will do this primarily through a graphical comparison but will provide a numerical result as well.

Using the code in problem2.m, we obtained a numerical error result of 6.609296443471653e-16 at \(x=2m\). As expected, this numerical result is close to machine roundoff since our derivative approximations are exact. Below we showcase a plot of our calculated solution (blue) against the correct solution (green). As you can see, the two solutions are indistinguishable to the eye and that, under only its own weight, the beam's deflection at 2 meters is small.

We will now proceed to analyze our calculated solutions for various discretization widths in Problem 3

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