The twice-differentiable functions fand g are defined for all real numbers x. Values of f, f', g, and g'for various values of x are given in the table below. -2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 30E
icon
Related questions
Question

Question & close up of chart are attached as images. Please show your work for each part, thank you!

The twice-differentiable functions f and g are defined for all real numbers x. Values of f, f', g,
and g'for various values of x are given in the table
below.
-2
-2 <x<-1
-1
-1 <x<1
1<x<3
3
12
Positive
Positive
2
Posiive
a) Find the x- and y-coordinate of each relative
minimum of fon the interval [-2, 3]. Justify your
-5
Negative
Negative
Positive
g(x)
-1
Negative
Positive
3
Positive
answers.
g'(x)
2
Positive
Positive
Negative
-2
GA
b) Let h(x) = [*, g(t)dt. Find all intervals where h(x) is concave up. Justify your answers.
1/2
m/2
Transcribed Image Text:The twice-differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'for various values of x are given in the table below. -2 -2 <x<-1 -1 -1 <x<1 1<x<3 3 12 Positive Positive 2 Posiive a) Find the x- and y-coordinate of each relative minimum of fon the interval [-2, 3]. Justify your -5 Negative Negative Positive g(x) -1 Negative Positive 3 Positive answers. g'(x) 2 Positive Positive Negative -2 GA b) Let h(x) = [*, g(t)dt. Find all intervals where h(x) is concave up. Justify your answers. 1/2 m/2
The twice-differentiable functions f and g are defined for all real numbers x. Values of f, f', g,
and g'for various values of x are given in the table
below.
-2
-2 <x<-1
-1
-1 <x<1
1<x<3
3
12
Positive
Positive
2
Posiive
a) Find the x- and y-coordinate of each relative
minimum of fon the interval [-2, 3]. Justify your
-5
Negative
Negative
Positive
g(x)
-1
Negative
Positive
3
Positive
answers.
g'(x)
2
Positive
Positive
Negative
-2
GA
b) Let h(x) = [*, g(t)dt. Find all intervals where h(x) is concave up. Justify your answers.
1/2
m/2
Transcribed Image Text:The twice-differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'for various values of x are given in the table below. -2 -2 <x<-1 -1 -1 <x<1 1<x<3 3 12 Positive Positive 2 Posiive a) Find the x- and y-coordinate of each relative minimum of fon the interval [-2, 3]. Justify your -5 Negative Negative Positive g(x) -1 Negative Positive 3 Positive answers. g'(x) 2 Positive Positive Negative -2 GA b) Let h(x) = [*, g(t)dt. Find all intervals where h(x) is concave up. Justify your answers. 1/2 m/2
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill