Question: The profit of a company can be modelled by the polynomial function P(t) = -t^3 +12t^2 -21t +10, where P is the profit in thousands of dollars, and t is the time in years. When will the company make their maximum profit of $108, 000?

I have seen some solutions that begin as :

dp/dt = -3t^2+24t-21

However, I'm unsure what dp/dt means and how to calculate this. Please let me know the steps to calculating dp/dt.