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Lecture

ECO 302 Lecture 04.docx

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School
Department
Economics
Course
ECO 302
Professor
Nicole Nelson
Semester
Fall

Description
Review of Basic Calculus (1) The Difference Quotient: Δ y= f (x+∆ x)−f (x) Δx ∆x dy (2) The derivative of the function y = f(x), which is written as dx or f (x) is dy f (x+∆x)−f (x) dx =l∆→0 ∆ x assuming the limit exists. (3) Basic rules: Power Rule f (x)= x n The derivative for the function dy n−1 f′(x)= =nx dx f (x) = x f (x) = 2x−1= 2x = 2x i.e Sums and Differences If f(x) and g(x) are both differentiable, then the sum and difference are differentiable. F(x) = f (x)+ g(x) and G(x) = f (x)− g(x) Hence dF dF dx = F (x) = f (x)+ g (x) dx = F (x) = f (x)− g (x) Products F(x) = f(x).g(x) F (x) = f (x).g(x)+ g (x).f (x) The derivative: 3 2 3 2 y = (x −10)x f (x) = x −10 g(x) = x 2 f (x) =3x g (x) = 2x F (x) =3x .x +2x(x −10)3 (4) The second derivative of a function Y = f(x) d y f (x) 2 Denot
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