Let f(x) = 2x³ − ²x² – 3 1. Find the first derivative of the function. (This function can be easily factored without using the quadratic formula). f'(x) = 6x²-x 6x²-x=0 X(6x-1) X=0) 6x-1 6x= x=½ 2. Where are the relative extrema, if they exist? Show all parts of the analysis necessary to determine these point(s). Label everything you do. 3. Find the second derivative of the function. (This function can be easily factored without using the quadratic formula).

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...
Question
Let f(x) = 2x³ – x² – 3
1. Find the first derivative of the function. (This function can be easily factored
without using the quadratic formula).
6x²-x=0
X (6x-1) X=0) 6x-1=
x=1
6x=1
6
2. Where are the relative extrema, if they exist? Show all parts of the analysis
necessary to determine these point(s). Label everything you do.
f'(x) = 6x²-x
3. Find the second derivative of the function. (This function can be easily factored
without using the quadratic formula).
4. Find the inflection point(s), if there are any. Show all parts of the analysis
necessary to determine these point(s).
Transcribed Image Text:Let f(x) = 2x³ – x² – 3 1. Find the first derivative of the function. (This function can be easily factored without using the quadratic formula). 6x²-x=0 X (6x-1) X=0) 6x-1= x=1 6x=1 6 2. Where are the relative extrema, if they exist? Show all parts of the analysis necessary to determine these point(s). Label everything you do. f'(x) = 6x²-x 3. Find the second derivative of the function. (This function can be easily factored without using the quadratic formula). 4. Find the inflection point(s), if there are any. Show all parts of the analysis necessary to determine these point(s).
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