Let f be a function in C (R), infinitesimal as x + 0 and with a minimum point at x =0. Then necessarily %3D O (A)f(x) = h+ kx² + o(x²), h, k E (0, +0) O (B) f(x) = kx² + o(x²), ke (0, +o0) O (C)f(x) = kx* + o(x*), kE (0, +o0) O (D) f'(0) = 0, and f'(x) 20 %3D %3D O (E) the smallest order of the derivative that is non-zero at x = O is even

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 15BEXP
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Let f be a function in C (R), infinitesimal as x + 0 and with a minimum point at x = 0 Then necessarily
%3D
O (A) f(x) = h+ kx? + o(x²), h, k E (0, +0)
O (B) f(x) = kx² + o(x²), k e (0, +o0)
O (C)f(x) = kx* + o(x*), k E (0,+o0)
O (D)f'(0) = 0, and f'(x) >0
%3D
%3D
%3D
O (E) the smallest order of the derivative that is non-zero at x
%3D
O is even
Transcribed Image Text:Let f be a function in C (R), infinitesimal as x + 0 and with a minimum point at x = 0 Then necessarily %3D O (A) f(x) = h+ kx? + o(x²), h, k E (0, +0) O (B) f(x) = kx² + o(x²), k e (0, +o0) O (C)f(x) = kx* + o(x*), k E (0,+o0) O (D)f'(0) = 0, and f'(x) >0 %3D %3D %3D O (E) the smallest order of the derivative that is non-zero at x %3D O is even
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