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Work Problems ( a) Let ) f(x) = x² - 6x³ + 12x² - 16x - 65. Find the concavity and the inflection point(s) of f(x).

Work Problems ( a) Let ) f(x) = x² - 6x³ + 12x² - 16x - 65. Find the concavity and the inflection point(s) of f(x).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Work Problems ( a) Let ) f(x) = x² - 6x³ + 12x² - 16x - 65. Find the concavity and the inflection point(s) of f(x). b) Let f(x) = √x³ (x − 2)². .) i) Fully explain why f(x) has an absolute minimum and an absolute maximum on the interval [-2, 16]. ii) Find the absolute minimum of f(x) on the interval [-2, 16]. c) Let 5x²y² - 3√x = 4x – 2y. ( i) Using implicit differentiation find dy dx ii) Find the equation of the tangent line at P(1, 1).
Transcribed Image Text:Work Problems ( a) Let ) f(x) = x² - 6x³ + 12x² - 16x - 65. Find the concavity and the inflection point(s) of f(x). b) Let f(x) = √x³ (x − 2)². .) i) Fully explain why f(x) has an absolute minimum and an absolute maximum on the interval [-2, 16]. ii) Find the absolute minimum of f(x) on the interval [-2, 16]. c) Let 5x²y² - 3√x = 4x – 2y. ( i) Using implicit differentiation find dy dx ii) Find the equation of the tangent line at P(1, 1).
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