The measles pathogenesis function $f(t)=-t^3+20t^2+21t$ models the development of the disease, where $t$ is measured in days and and $f(t)$ represents the number of infected cells per milliliter of plasma.

a$)$ What is the peak infection time $($ t $)$ for the measles virus?

b$)$ What is the number of infected cells permilliliter at this time?

Explain how you got your answer and why.

PLEASE SHOW ALL STEPS