Summary TUTORIAL 8A MEMO

STK120 – 162 TUT 8A MEMO
Question 1 (TUT 8A)
Find the derivative:

a) 𝑦 𝑥 3
𝑑𝑦
2𝑥
𝑑𝑥
b) 𝑤 3𝑧
𝑑𝑤
6𝑧 𝑧
𝑑𝑧
c) 𝑓 𝑥 √𝑥 2𝑥 4𝑥 1
1
𝑓 𝑥 √𝑥 2𝑥 8𝑥 4𝑥 1 𝑥 2
2
d) 𝑓 𝑥
5𝑥 3 2𝑥 𝑥 1 5
𝑓 𝑥
5𝑥 3

e) 𝑓 𝑥 √𝑥 2𝑥 1
1
𝑓 𝑥 𝑥 2𝑥 1 3𝑥 2
2
f) 𝑓 𝑥
𝑥 1 𝑥 3 .1 𝑥 1 .1 𝑥 1 4 12 𝑥 1
𝑓 𝑥 3 3
𝑥 3 𝑥 3 𝑥 3 𝑥 3 𝑥 3

g) 𝑓 𝑥 ln 5𝑥 3
10𝑥
𝑓 𝑥
5𝑥 3
h) 𝑓 𝑥 𝑒
𝑓 𝑥 𝑒 6𝑥
i) Calculate the second order derivative of 1(h)
𝑓 𝑥 𝑒 6 𝑒 6𝑥 6𝑥 6𝑒 36𝑥 𝑒

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.
𝐶 6 𝐶 3 38 20
𝐴𝑅𝐶 6 ∗ 1000 6000
6 3 3
If between 300 and 600 units are produced, then the cost is increasing on average by R6000 per
100 units.