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Unformatted text preview: Lecture 1  Math Review. Topics from Calculus you should know: How to define a derivative How to interpret f ( x ) = 2. What does that mean? How to calculate the derivative of: 1 polynomials, ex.: u ( x ) = 3 x 4 5 x 2 + 6 2 exponential functions, ex.: u ( x ) = e x 2 + 2 3 logrithmic functions, ex.: u ( x ) = x ln ( 3 x + 6 ) Know the product rule, quotient rule, and chain rule Implicit differentiation ECG 700 Lecture 1  Math Review 1/ 18 Lecture 1  Math Review. Topics from Calculus you should know (cont.): The first derivative test. The second derivative test. Partial derivatives Total differentiation Topics you probably dont know but will learn: Legrange multipliers Envelope Theorem ECG 700 Lecture 1  Math Review 2/ 18 Differentiation  a quick review Definition The derivative of a function at a: d dx f ( a ) = f ( a ) = lim x a f ( x ) f ( a ) x a or equivalently: f ( a ) = lim h f ( a + h ) f ( a ) h ECG 700 Lecture 1  Math Review 3/ 18 Differentiation  a quick review What does the derivative represent? The slope of the tangent line at point a. The instantaneous rate of change For our purposes, marginal = derivative . The marginal utility of good x is the change in utility resulting from a change to the quantity of good x ....
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 Fall '09
 Morrill

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