Given the equation wt231 1932t2 where t is measured in years

Given the equation: w(t)=23.1 +19.32t^2, where t is measured in years and w(t) is measured in kilograms. Find the time t when the instantaneous rate of change in a pup\'s mass is the same as the average rate of change. You need not simplify your answer.

Solution

Given the equation: w(t)=23.1 +19.32t^2

differentiate the equation, we get

dw/dt = 0 + 2[19.32]*t

= [38.64]t

The average rate of change is 19.32. if the instantaneous rate of

change in a pup\'s mass is equal to the average rate of change, the

time t is,

   [38.64]t = 19.32

t = 0.5 s