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**a) Research the three finite difference approximations mentioned above (forward, backward and central). Use a spreadsheet to demonstrate each of these numerical methods for the function below.**

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y=x

^{3}−x^{2}+0.5xInvestigate the derivative over the range x = [0,1], using finite differences of 0.1

b)Plot the results from each method onto one graph, along with the analytical derivative of the function. Make sure your plot includes a legend.

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i can see that this is a really (really) easy question if you know how to utilise the finite differences method in excel, however as you can see from the question were weren't taught it and we have to research it, so i went to wikipedia (obviously!)

so anyway i see on wikipedia they have this:

which i can partially understand, you just insert your function where it says f(x) and then link you x values to a table of values 0-1 in 0.1 steps, but i don't understand what the "h" stands for, then for part b i guess by analytical derivative it means just standard differentiation so:

y=x

[tex]\stackrel{dy}{dx}[/tex]=3x

^{3}−x^{2}+0.5x[tex]\stackrel{dy}{dx}[/tex]=3x

^{2}-2x+0.5if anyone could lend a hand or a link to a good "dummies guide" web page I'd be very grateful.

Thanks

Elliott M