#2) Let X = R. Find a minimizer and maximizer of (P) for each the following data. If one or neither exist, produce minimizing and maximizing sequences. (i) X = R and f(x) = x² − 2x + 1. (ii) X = [0, 1] and f(x) = x² - 2x + 1. (iii) X = R and e*. (iv) X = (0, +∞0) and f(x) = -In(x). (v) X=[-, π] and f(x) = sin(x). (vi) X = (0, +∞) and f(x) = ¹. (vii) X = (0, +∞) and f(x) = 2x + 1. (viii) X=[-2,3] and f(x) = (x² - 1)²
#2) Let X = R. Find a minimizer and maximizer of (P) for each the following data. If one or neither exist, produce minimizing and maximizing sequences. (i) X = R and f(x) = x² − 2x + 1. (ii) X = [0, 1] and f(x) = x² - 2x + 1. (iii) X = R and e*. (iv) X = (0, +∞0) and f(x) = -In(x). (v) X=[-, π] and f(x) = sin(x). (vi) X = (0, +∞) and f(x) = ¹. (vii) X = (0, +∞) and f(x) = 2x + 1. (viii) X=[-2,3] and f(x) = (x² - 1)²
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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![#2) Let X = R. Find a minimizer and maximizer of (P) for each the following data.
If one or neither exist, produce minimizing and maximizing sequences.
(i) X = R and f(x) = x² - 2x +1.
(ii) X = [0, 1] and f(x)= x² - 2x + 1.
(iii) X = R and e.
(iv) X = (0, +∞o) and f(x) = -ln(x).
(v) X=[-, π] and f(x) = sin(x).
(vi) X = (0, +∞) and f(x) = 1.
(vii) X = (0, +∞) and f(x) = 2x + ¹.
(viii) X=[-2,3] and f(x) = (x² - 1)²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadd5b56d-97e3-4d3c-9aa9-5b563ad77377%2F56419fd6-6f1b-424f-9244-b0d85309a293%2F8orgnvt_processed.png&w=3840&q=75)
Transcribed Image Text:#2) Let X = R. Find a minimizer and maximizer of (P) for each the following data.
If one or neither exist, produce minimizing and maximizing sequences.
(i) X = R and f(x) = x² - 2x +1.
(ii) X = [0, 1] and f(x)= x² - 2x + 1.
(iii) X = R and e.
(iv) X = (0, +∞o) and f(x) = -ln(x).
(v) X=[-, π] and f(x) = sin(x).
(vi) X = (0, +∞) and f(x) = 1.
(vii) X = (0, +∞) and f(x) = 2x + ¹.
(viii) X=[-2,3] and f(x) = (x² - 1)²
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