Discrete Network Telemetry (Computer & Systems Engineering)

A network systems engineer is monitoring the cumulative data transferred, $D$ (in Gigabytes), over a cloud server during a traffic spike. A network interface controller samples the total data transferred at discrete times $t$ (in seconds), summarized in the table below:

1. Calculate the average data transfer rate (in GB/s) over the intervals $[10, 14]$ and $[12, 14]$ using the discrete data from the table.
2. If the data transfer profile is modeled continuously by $D(t) = 1.5t^2 - 5t + 50$, use the secant slope limiting process over the shrinking intervals $[14, 14.1]$, $[14, 14.01]$, and $[14, 14.001]$ to estimate the instantaneous data transfer rate (throughput) at exactly $t = 14$ seconds.