Fundamental Methods of Mathematical Economics

see attached file

ECON3410 Sec.MY2

Fundamental Methods of Mathematical Economics I

– Final Exam –

Due 12 noon, May 27, 2013

– Show the process of your calculation as fully as possible. This is also for your partial points if you
get wrong. You won’t earn any points for only final answers. You are not allowed to discuss the exam
with the other students. If you have any questions, just feel free to ask me by email.
– To sumbmit your exam, please scan your answers and email me at hmoritajpgmail.com. The subject
line must be ”ECON3410 FINAL EXAM.”

Part I

(1) Find a derivative of y = (8×3 + 3×2 + 1)10

(2) Find a derivative of y = (x2 + 4x + 1)(3×2 − 4)

(3) Find a derivative of f(x) = e−5

x

3
+2x

(4) Find a derivative of y =
3×2 + 2

x − 2

(5) Find a derivative of f(x) = (x − 1)2(x + 6)4

(6) Find a derivative of y =
3

√

x2 − 1

(7) Find a derivative of ln(x2 + 1)

(8) Find a derivative of y =
6×2 + 2x + 3

√
x

Part II: In this part, you need to choose the numbers for the Greek characters before answering
the questions.

(9) Using its definition:
dy

dx
= lim

h→0

f(x + h) − f(x)

h
, find the derivative of y = αx2 + β + γ. Choose

any 3 distinct integers for α, β, and γ

(10) Suppose that Company A’s production has the following (total) cost function: c(q) = q4+βq3−10
where c is a total cost in dollars and q is a quantity to produce. Find a marginal cost when q = δ.
Choose any integer between 10 and 100 for β, and any decimal greater than 10.00 for δ