What is the inflection point of the graph of f(x) = x³ – 3x??O The point of inflection is (1, -2).O The point of inflection is (3, 0).O The point of inflection is (-1, -3).O The point of inflection is (0, 0).

Name: What is the inflection point of the graph of f(x) = x³ – 3x??O The po
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Description: What is the inflection point of the graph of f(x) = x³ – 3x??O The point of inflection is (1, -2).O The point of inflection is (3, 0).O The point of inflection is (-1, -3).O The point of inflection is (0, 0).

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 15T

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What is the inflection point of the graph of f(x) = x³ – 3x??
O The point of inflection is (1, -2).
O The point of inflection is (3, 0).
O The point of inflection is (-1, -3).
O The point of inflection is (0, 0).

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$T h e v a l u e o f x f o r i n f l e c t i o n p o i n t i s c a l c u l a t e d a t f'' (x) = 0 . G i v e n f u n c t i o n f (x) - f (x) = x^{3} - 3 x^{2} D i f f e r e n t i a t i n g o n b o t h s i d e s w i t h r e s p e c t t o' x' - f' (x) = \frac{d}{d x} (x^{3} - 3 x^{2}) f' (x) = 3 x^{(3 - 1)} - 3 (2) x^{(2 - 1)} [\frac{d}{d x} x^{n} = n x^{(n - 1)}] f' (x) = 3 x^{2} - 6 x A g a i n d i f f e r e n t i a t i n g w i t h r e s p e c t t o' x' - f'' (x) = \frac{d}{d x} (3 x^{2} - 6 x) f'' (x) = 3 (2) x^{(2 - 1)} - 6 (1) x^{(1 - 1)} f'' (x) = 6 x - 6 . . . . . . . . . . . . . . . . . . . . (1)$

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