Nuclear magnetic resonance (NMR) is a common method for determining the chemical composition of samples. Different compounds absorb electromagnetic radiation at a frequency characteristic of the compound. Thus, if the amount of radiation absorbed is plotted against frequency, the peak positions impart vital information about the composition of the sample. Below are some hypothetical data, D(x), measured against the variable x.

a. Plot the data.

b. Approximate the derivative of D(x) using two different methods.

c. Hence estimate where the peak is in the data. Compare your results of the two different methods, and discuss which method is better for this particular set of data and why.