Calculus Self Test/ Study Guide

Short Description
Calculus Self Test/ Study Guide. This handout presents many of the calculus concepts that will be used in E110. (Suggestions, look up concepts in your old …

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Content
Economics 110, Section 2 Due: Noon, September 8, 2006
Name ____________________
Calculus Self Test/ Study Guide
This handout presents many of the calculus concepts that will be used in E110.
(Suggestions, look up concepts in your old calculus text or check out Tvestlanka
Karagyozova’s CalculusReview at:
http://mlovell.web.wesleyan.edu/EconCalc/KaragyozovaCalcReview.pdf)
Please deposit your completed Self-Test in the E110 Section 2 slot in the White Lock
Box in the alcove around the corner from the Econ Office (123 PAC) as soon as possible
- by 12:00 noon, on Friday, September 8th, at the latest.
1. Differentiate the following functions:
a. y(x) = 36 - 2×2
b. z(x) = (6 - 2x)(x2)
c. f(x) = (ax2 + b)3
d. y = ln x (ln x denotes the log of x to the base e)
e. y = 2 ln(x3)
f. a(r) = ?r2Economics 110, Section 2 Calculus Review Due: September 8, 2006
2. Consider the function y(x) = 72 + 8x - 2×2, (0 < x < 6)
a. Fill in the blanks in the following table
b. Determine, using the calculus, the value of x, call it x0 that yields the
maximum value of y(x). Show your work. Explain!
c. Determine the second derivative, d2y/dx2
, at point x0.
d. Explain why it is important to consider the sign of d2y/dx2
evaluated at x0.
x 0 1 2 4 5 6
y(x) 72 ______ ______ ______ 62 __48
dy/dx ______ ______ ______ -8 ______ ___-16_
dy2/dx2 ______ ______ ______ ______ ______ __-4...