5. Prove that f has a zero of order m at zo if and only if f(zo), ƒ'(zo),...‚ ƒ(m-¹) (zo) are all equal to zero, but f(m) (zo) ‡0.
5. Prove that f has a zero of order m at zo if and only if f(zo), ƒ'(zo),...‚ ƒ(m-¹) (zo) are all equal to zero, but f(m) (zo) ‡0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.1: Polynomial Functions Of Degree Greater Than
Problem 55E
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![5. Prove that f has a zero of order m at zo if and only if f(zo), ƒ'(zo),...‚ ƒ(m-¹) (zo)
are all equal to zero, but f(m) (zo) ‡0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3688a312-1b6e-40d4-973f-537807921925%2F7d6ff570-e1fb-419e-8e20-61e877fb743e%2Fbvcsnde_processed.png&w=3840&q=75)
Transcribed Image Text:5. Prove that f has a zero of order m at zo if and only if f(zo), ƒ'(zo),...‚ ƒ(m-¹) (zo)
are all equal to zero, but f(m) (zo) ‡0.
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