A mouse runs through a maze in less than a minute the first time it tries. Its times got better for a while with each new try but then got worse(it took longer) due to fatigue. If the time to complete the maze on the nth try can be modeled by the equation t(n)=0.4n^2-8n+50, where n is the number of the trial and t is the time it takes to complete the trial(in seconds). a) use the definition of derivative as a difference quotient to find the instantaneous rate of change of t at trial n.
b) Use Calculus to determine which trial was the fastest
c) compare the average rate of change in time to complete the maze from trial 1 to trial 5 with the instantaneous rate of change in completion time at trial 5.