High CPU and memory usage from .NET MVC application

We see a very large amount of CPU and memory usage from one of our .NET MVC applications, and it seems we cannot determine the reason for this. Our group does not have access to the web server itself, but instead receives a notification automatically when certain limits are reached (90 %% of the processor or memory). By running locally, we cannot find the problem. Some items that we think may be the culprits

• The application has several threads running in the background when users take certain actions.
• We use memcached (on a different machine than the web server).
• We use web sockets

Also, the application is pretty standard as web applications go. Here are a couple of forms, login / logout, some administrator features for managing users and data; nothing supernatural.

I consider two different solutions and wonder what would be better.

• Create a page inside the application itself (available only to application administrators) that displays information about the used memory and CPU. Are there any examples of this or is it even possible?
• Use some type of third-party profiling service or application that is installed on web servers and allows us to go down to find what causes a high level of CPU and memory usage in the application.