Method for detecting anomalies in timeseries?

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I am exploring creating alerts for anomalies in a timeseries. Say that I have a graph like this:

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There are two anomalies here that I would wanted to be alerted on: First, on April 7th with there was a huge spike away from the mean. Second, around May 28th, when it's clear that the data is on a downward trend. I am looking for resources that explain algorithms for detecting these kinds of anomalies - does anyone know of any?

Also - I do know that some alert-generating software exists (Nagios and Tableau.) Is there any software that will create alerts like I am describing?

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It looks like you have two low days (weekend?) and five days (work week?) which is concave.

You might subtract the mean (say) of the low values from the next five and look at the resulting points. If the resulting segments are usually similar, the ones that are not (such as May 19 through May 25) might be worth looking at.

I could make all sorts of suggestions based on the effects of various types of organizational activities, but I will refrain.