The University of Papua New Guinea
Quantitative Economics 1, Semester 2.
2022
Tutorial 6.
Question 1. Given the function 𝑦 = 4𝑥 2 + 9
a.
Find the difference quotient as a function of x and 𝜕x. Use x in lieu of 𝑥0
b.
Find the Derivative of
c.
Find f’ (3) and f’ (4)
𝑑𝑦
𝑑𝑥
Question 2. Find the derivative of each of the following functions.
1
a.
b.
c.
d.
𝑦 = 𝑥2
𝑦 = 63
𝑦 = 7𝑥 5
𝑤 = 3𝑢−1
e.
𝑤 = −4𝑢2
f.
𝑤 = 4𝑢4
1
1
Question 3 Given the total cost function TC = 𝑸𝟑 − 𝟓𝑸𝟐 + 𝟏𝟐𝑸 + 𝟕𝟓, Write out a
variable-cost (VC) function. Find the derivative of the VC function, and interpret the
economic meaning of that derivative.
Question 4. Given the average cost function, AC = 𝑸𝟐 − 𝟒𝑸 + 𝟏𝟕𝟒 find the MC function.
Is the given function more appropriate as a long-run or a short-run function? Why?
Question 5. Differentiate the following by using the product rule;
a.
(9𝑥 2 − 2)(3𝑥 − 1)
b.
(3𝑥 + 10(6𝑥 2 − 7𝑥)
c.
𝑥 2 (4𝑥 + 6)
d.
(𝑎𝑥 − 𝑏)(𝑐𝑥 2 )
e.
(2 − 3𝑥)((1 + 𝑥)(𝑥 + 2)
f.
(𝑥 2 − 3)𝑥 −1
Question 6. Find the Derivative of:
a.
b.
c.
d.
𝑥 2 +3
𝑥
𝑥+9
𝑥
(
6𝑥
𝑥+5
)
𝑎𝑥 2 +𝑏
𝑐𝑥+𝑑