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Two functions g(x) and h(x) have derivatives g'(x)=2x2-10x+8 and h'(x)=6x-16. The graphs of g'(x) and h'(x) are given below. h'(x) 2 g'(x) Note that the formulas and graphs of g(x) and h(x) are not given. (a) Find all values of x at which the graph of g(x) has a horizontal tangent line. smaller x= larger x= (b) Find all values of x at which the graph of g'(x) has a horizontal tangent line. X= (c) Name the longest interval over which g(x) is increasing and h(x) is decreasing. from x= to x= (d) Find the value of x where the graph of h(x) is lowest. (e) Which of the following is true about the graph of g(x) on the interval from x=0 to x=1? (Select only one.) O The graph of g(x) is highest at x=1 because g(x) is increasing from x=0 to x=1. O The graph of g(x) is highest at x=0 because g'(x) is decreasing from x=0 to x=1. O The graph of g(x) is highest at x=1 because g'(x) is increasing from x=0 to x=1. The graph of g(x) is highest at x=0 because g(x) is decreasing from x=0 to x=1.

Two functions g(x) and h(x) have derivatives g'(x)=2x2-10x+8 and h'(x)=6x-16. The graphs of g'(x) and h'(x) are given below. h'(x) 2 g'(x) Note that the formulas and graphs of g(x) and h(x) are not given. (a) Find all values of x at which the graph of g(x) has a horizontal tangent line. smaller x= larger x= (b) Find all values of x at which the graph of g'(x) has a horizontal tangent line. X= (c) Name the longest interval over which g(x) is increasing and h(x) is decreasing. from x= to x= (d) Find the value of x where the graph of h(x) is lowest. (e) Which of the following is true about the graph of g(x) on the interval from x=0 to x=1? (Select only one.) O The graph of g(x) is highest at x=1 because g(x) is increasing from x=0 to x=1. O The graph of g(x) is highest at x=0 because g'(x) is decreasing from x=0 to x=1. O The graph of g(x) is highest at x=1 because g'(x) is increasing from x=0 to x=1. The graph of g(x) is highest at x=0 because g(x) is decreasing from x=0 to x=1.

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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Two functions g(x) and h(x) have derivatives g'(x)=2x2-10x+8 and h'(x)=6x-16. The graphs of g'(x) and h'(x) are given below. y h'(x), 2 g'(x) Note that the formulas and graphs of g(x) and h(x) are not given. (a) Find all values of x at which the graph of g(x) has a horizontal tangent line. smaller x= larger x= (b) Find all values of x at which the graph of g'(x) has a horizontal tangent line. X= (c) Name the longest interval over which g(x) is increasing and h(x) is decreasing. from x= to x= (d) Find the value of x where the graph of h(x) is lowest. X= (e) Which of the following is true about the graph of g(x) on the interval from x=0 to x=1? (Select only one.) O The graph of g(x) is highest at x=1 because g(x) is increasing from x=0 to x=1. The graph of g(x) is highest at x=0 because g'(x) is decreasing from x=0 to x=1. The graph of g(x) is highest at x=1 because g'(x) is increasing from x=0 to x=1. The graph of g(x) is highest at x=0 because g(x) is decreasing from x=0 to x=1.
Transcribed Image Text:Two functions g(x) and h(x) have derivatives g'(x)=2x2-10x+8 and h'(x)=6x-16. The graphs of g'(x) and h'(x) are given below. y h'(x), 2 g'(x) Note that the formulas and graphs of g(x) and h(x) are not given. (a) Find all values of x at which the graph of g(x) has a horizontal tangent line. smaller x= larger x= (b) Find all values of x at which the graph of g'(x) has a horizontal tangent line. X= (c) Name the longest interval over which g(x) is increasing and h(x) is decreasing. from x= to x= (d) Find the value of x where the graph of h(x) is lowest. X= (e) Which of the following is true about the graph of g(x) on the interval from x=0 to x=1? (Select only one.) O The graph of g(x) is highest at x=1 because g(x) is increasing from x=0 to x=1. The graph of g(x) is highest at x=0 because g'(x) is decreasing from x=0 to x=1. The graph of g(x) is highest at x=1 because g'(x) is increasing from x=0 to x=1. The graph of g(x) is highest at x=0 because g(x) is decreasing from x=0 to x=1.
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