1. Find the second derivative of f(x), then find the x-values at which f(x) is concave up and the x-values at which it is concave down. Remember that you do this by figuring out where the second derivative is positive or negative. So if you for example found the second derivative to be f"(x) = 2x+6 then you would find where it is concave up by solving 2x+6> 0 for x and you would find where it is concave down by solving 2x+6 < 0 for x. A. f(x) = 3x^3+12x^2+5x+7 B. f(x) = 2x^2+5x+7 [hint: this function will always be either concave up or concave down-which is it?]

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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1. Find the second derivative of f(x), then find the x-values at which f(x) is concave up and the x-values at which it is
concave down. Remember that you do this by figuring out where the second derivative is positive or negative. So
if you for example found the second derivative to be f"(x) = 2x+6 then you would find where it is concave up by
solving 2x+6 > 0 for x and you would find where it is concave down by solving 2x+6 < 0 for x.
A. f(x) = 3x^3+12x^2+5x+7
B. f(x) = 2x^2+5x+7 [hint: this function will always be either concave up or concave down-which is it?]
Transcribed Image Text:1. Find the second derivative of f(x), then find the x-values at which f(x) is concave up and the x-values at which it is concave down. Remember that you do this by figuring out where the second derivative is positive or negative. So if you for example found the second derivative to be f"(x) = 2x+6 then you would find where it is concave up by solving 2x+6 > 0 for x and you would find where it is concave down by solving 2x+6 < 0 for x. A. f(x) = 3x^3+12x^2+5x+7 B. f(x) = 2x^2+5x+7 [hint: this function will always be either concave up or concave down-which is it?]
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