Configure/Optimize my server to handle high traffic stably (Using Wordpress site)

My wordpress site always goes down (gives 500 Internal Server Error) during high traffic which is around 10,000 concurrent users. My dedicated server should handle that easily. Specs for the dedi server are, Intel Xeon E3-1240V2 24GB RAM Intel 520 Series SSD cPanel/WHM Linux CentOS I asked my host to switch to Nginx because I look it up online and found many people including [login to view URL] switched to Nginx for faster performance. It didn't work. Still the same thing. I am also using WP-Super Cache plugin. So, I need someone trusted and certified to handle this by configuring/optimizing on my server to make any necessary changes to solve this issue.