How to determine the optimal number of clusters?

Question

[melissachua90]

Here, I have a plot of the Cluster Prediction Index and Gap-Statistics for a range of 2:8 clusters.

How do I identify the optimal number of clusters? Should it be the highest point in both plots? In this image, what would the optimal number be?

[seidel]

Do you have a definition of optimal? Do you have a context in which something can be more optimal or less optimal? Can you provide any more information or context so that someone could understand this graph or how or why it's generated?