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1. Trovare gli zeri delle seguenti funzioni: (a) f (x) = x2 − 2x + 1 (b) f (x) = x2 − 3x + 1 (c) f (x) = x2 − 3x + 4 (d) f (x) = x3 − 2x2 + x, (e) f (x) = x3 − x2 − x + 1 (nota che x = 1 `e uno zero)

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Horizon (0, ∞) y = x2 (0, 0)

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Practice Problems on Gradients and Directional Derivatives p 1) Consider the function f (x, y) = ln( x2 + y 2 ). Find its gradient at the point (x, y) = (1, −1). At this point, what is the directional derivative of f i

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• Analytic geometry
• Differential calculus
• Elementary mathematics
• Vector calculus
• Generalizations of the derivative
• Gradient
• Derivative
• Slope
• Dimensional analysis
• Mathematics
• Mathematical analysis
• Calculus

Midterm Exam, Econ 210, Fall 2009 Answer Question 1 and any 3 of the other questions. Question 1. Mary Granola consumes only two goods and her utility function is 2 U (x1 , x2 ) = (min{2x1 + x2 , x1 + 2x2 }) .

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