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10fB_ps00

# 10fB_ps00 - see if each critical point is a maximum minimum...

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Microeconomics ECON 100A Problem Set 0 Due September 29, 2010 (Solutions Posted October 1, 2010) Professor Michael Noel University of California San Diego 1. Find the first and second derivatives for the following functions of x. a. f(x) = a + bx + cx 2 + dx 3 b. f(x) = ln(4x 3 ) 2. Let z = 4x 4 y 3 - 5x 2 y + xy 2 a. Derive the first and second partial derivatives for z. What is true about the cross partials? b. Derive the total differential of z. 3. Find the critical points of the following functions and check the second order conditions to
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Unformatted text preview: see if each critical point is a maximum, minimum, or a saddle point.: a. f(x) = - (1-x) 2 b. f(x) = (1 - x) 2 c. f(x) = (1-4x)x – 3x 2 d. f(x) = x 3 + 1 where f is defined over x in [0,1]; 4. This question is very, very, very important. We will be doing problems like this one all the time. Maximize the following functions subject to the given constraint. a. f(x,z) = xz subject to x + z ≤ 2 b. f(x,z) = x 1/2 z 1/2 subject to p x x + p z z ≤ Y...
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