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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.
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