Nelly works part-time in a shop to cover her university expenses.
The table below shows how many
hours she worked each day last week.
Nelly's weekly pay is worked out
as follows: Monday to Friday
• £8 per hour for the first 15 hours
• £10 per hour for any extra hours
Saturday
• double the normal rate of £8 per hour
Hours worked
372
5
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Work out Nelly's total pay for last week.
You must show all your working.
22 hours
-15x8= 120
212
4
2
5

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0