1. In the class, we showed that the first-order derivative of a function, P, with respect to the independent variable, x, can be approximately calculated using the forward difference:
$\frac{dP}{dx} \approx \frac{P(x + \Delta x) - P(x)}{\Delta x}$
We also used the Taylor series to show that the forward difference approximation has a first-order accuracy, O($\Delta$x), which means that its truncation error is proportional to the value of $\Delta$x.
Note that the backward finite difference approximation is written as:
$\frac{\partial P}{\partial x}(x) = \frac{P(x) - P(x - \Delta x)}{\Delta x}$
Please also use the Taylor series method to prove that the backward finite difference has a first-order accuracy, O($\Delta$x).
