I'm going to rewrite f(t) to make it a little easier to use the power rule:

Now just take the derivative using the power rule:

Since they ask for f'(a), we need to replace the t's with a's:
<span>On the first roll, the probability of rolling a 2 is 1/6.
On the second roll the probability of rolling a 3 is also 1/6, and the probability of rolling a 4 on the third roll is, you guessed it, 1/6.
Therefore the required probability is given by:
1/6 x 1/6 x 1/6 = 1/216</span>
10(the number of tests) divided by 5(the amount of weeks)=2. That is 2 tests every week. 2x7 weeks is 14 tests.
Or this could be a trick question and he could have only had tests for 5 weeks.