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Summary TUTORIAL 8A MEMO

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Master STK120 with Confidence! Stressed about acing your STK120 exams and tests? We've got the ultimate study pack to boost your understanding and exam performance. Our comprehensive collection of past STK120 tutorial papers and detailed memos provides valuable insights into exam format, key c...

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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.

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