In the first case, we desire to know \(f'(x)\text{,}\) the derivative of a function \(f\) for some value of \(x\text{.}\) Although most functions can be easily differentiated, if it is too complicated often a numerical derivative is sought instead or as we will see the function is not known.
for some continuous function \(f\text{.}\) This is an important skill in that we don’t need to look very far to find functions that we can’t take the antiderivative of. In such a case, we will resort to numerical integration or quadrature.
