A certain bacteria culture is growing so that it has a mass of 1/2t^2 + 1 grams after t hours.

a. How much did it grow during the interval [2, 2.01]?

b. What was its average growth rate during this interval [ 2, 2.01]?

c. What was its instantaneous growth rate at t=2?

What I first did is to differentiate the equation 1/2t^2 + 1, but what i got for my answer was t. From that, I subtracted 2. from 2.01 and got 0.01 for letter a, for letter b the average growth rate I did the same thing as for letter a but over its difference and got an answer of 1. Plz tell me if my procedures are correct and how to do c. I'll greatly appreciate it...