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(a) Find the stationary points of the following functions, and classify them: (i) f(x) = 3xe²™ (ii) g(x) = ln (x² − 4x + 5)

(a) Find the stationary points of the following functions, and classify them: (i) f(x) = 3xe²™ (ii) g(x) = ln (x² − 4x + 5)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. (a) Find the stationary points of the following functions, and classify them: (i) f(x) = 3xe²x (ii) g(x) = ln (x² - 4x + 5) (b) Under what circumstances are the first order conditions h₁(xo, yo) = 0 and h₂ (xo, yo) = 0 necessary but not sufficient to guarantee a maximum point for a function h(x, y) defined over a convex set S? Why is it that under these circumstances the first order conditions are not sufficient to guarantee a maximum point, and under what circumstances are they sufficient?
Transcribed Image Text:1. (a) Find the stationary points of the following functions, and classify them: (i) f(x) = 3xe²x (ii) g(x) = ln (x² - 4x + 5) (b) Under what circumstances are the first order conditions h₁(xo, yo) = 0 and h₂ (xo, yo) = 0 necessary but not sufficient to guarantee a maximum point for a function h(x, y) defined over a convex set S? Why is it that under these circumstances the first order conditions are not sufficient to guarantee a maximum point, and under what circumstances are they sufficient?
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