Answered: Find a, b, c, and d such that the cubic…

Find a, b, c, and d such that the cubic function f(x) = ax3 + bx2 + cx + d satisfies the given conditions. Relative maximum: (3, 23) Relative minimum: (5, 21) Inflection point: (4, 22)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section: Chapter Questions

Problem 3PT

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Question

100%

Find a, b, c, and d such that the cubic function

f(x) = ax³ + bx² + cx + d

satisfies the given conditions.

Relative maximum: (3, 23)
Relative minimum: (5, 21)
Inflection point: (4, 22)

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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