Consider the quadratic function g(x)=x²-4x+36. Define a new function S(x) by S(x)=the slope of the diagonal line through g(x) = 21. (a) Find the positive critical value of S(x). (b) Determine whether S(x) is concave up or concave down at the critical value you found in (a) and use the Second Derivative Test to determine if the critical value gives a local maximum or a local minimum. S(x) is ---Select-- A at the critical value. Therefore, the critical value gives a -Select-- e of S(x). (c) If x must be positive, what is the lowest possible value of S(x) ?
Consider the quadratic function g(x)=x²-4x+36. Define a new function S(x) by S(x)=the slope of the diagonal line through g(x) = 21. (a) Find the positive critical value of S(x). (b) Determine whether S(x) is concave up or concave down at the critical value you found in (a) and use the Second Derivative Test to determine if the critical value gives a local maximum or a local minimum. S(x) is ---Select-- A at the critical value. Therefore, the critical value gives a -Select-- e of S(x). (c) If x must be positive, what is the lowest possible value of S(x) ?
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...
Related questions
Question
Transcribed Image Text:Consider the quadratic function g(x)=-x²-4x+36.
Define a new function S(x) by
S(x)=the slope of the diagonal line through g(x) = IX.
(a) Find the positive critical value of S(x).
X=
(b) Determine whether S(x) is concave up or concave down at the critical value you found in (a) and use the Second Derivative Test to determine if the critical value gives a local maximum or a local minimum.
S(x) is ---Select---
+ at the critical value. Therefore, the critical value gives a ( ---Select---
A of S(x) .
(c) If x must be positive, what is the lowest possible value of S(x) ?
(d) If x is between 1 and 6, what are the largest and smallest possible values of S(x) ?
largest value of S(x) :
smallest value of S(x) :
(e) Give the longest interval over which S(x) is decreasing and g(x) is increasing.
from x=
to x=
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning