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e) 𝑓 𝑥 √𝑥 2𝑥 1
f) 𝑓 𝑥
g) 𝑓 𝑥 ln 5𝑥 3
h) 𝑓 𝑥 𝑒
i) Calculate the second order derivative of 1(h)
Question 2 (TUT 8A)
The cost function (in R1000) of a company is given by:
1
𝐶 𝑥 𝑥 2𝑥 3𝑥 20
3
with 𝑥 production (in 100 units).
a) Calculate the average rate of change when production increases from 300 to 600.
b) Calculate and interpret the instantaneous rate of change when 𝑥 4.
Question 3 (TUT 8A)
The demand for Nike trainers (in 100) in terms of its price (in R1000) is given by:
ln 𝑝
𝐷 𝑝
𝑝
where 𝑝 is price (in R1000) and 𝐷 is demand.
a) What is the units in which the income function will be measured?
b) Calculate the marginal demand function.
Question 4 (TUT 8A)
The demand function for cold drink is given by: 𝐷 𝑝 900 𝑝𝑙𝑛𝑝 where 𝑝 is the price
(in Rand) and 𝐷 𝑝 the demand in thousands. Calculate the marginal income when 𝑝 4.
Question 5 (TUT 8A)
The demand of a tin of cold drink at Cofi-on-Campus is given by the function:
.
𝐷 650𝑝𝑒
where D is the demand (in 1000) and p the price in Rand.
a. The marginal rate of change in the demand of the cold drink can be calculated by:
b. Calculate the marginal income function of a tin of cold drink.
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