b) What is the only critical point of this function? Explain.

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...
icon
Related questions
icon
Concept explainers
Topic Video
Question
100%
Question 2b
2. Now, as discussed in class, the absolute value function is formally defined as
z, if a 20
-{-3,if z<0
S(z) = |z| =
a) Sketch the graph of this function.
b) What is the only critical point of this function? Explain.
c) Would the critical point change in any way if we would consider g(x) = 2|x| instead
of f(x) = |x|? Explain why or why not.
3
3. Apply the Chain Rule and explain the differences among the following four ex-
amples from the point of view of differentiation. Compute explicitly each one of the
given derivatives:
(cos(5z)) =
Ccon(z")) =
dr
cos"(z) =
and
d
(cos(sin(5æ))) =
dz
4. Now, as explained in class, recall that some functions are defined implicitly by a
relation between z and y such as r² + y² = 4. In such cases, differentiating with respect
to a both sides helps us compute y'= 4. We should be careful, however, with the Chain
Rule that needs to be applied in the way. That is, if y is assumed to be a function of æ,
then
(y²)' = 2y(y/')
(e")' = (e")y/
and so on.
This process is called impne amerenciationr
Transcribed Image Text:2. Now, as discussed in class, the absolute value function is formally defined as z, if a 20 -{-3,if z<0 S(z) = |z| = a) Sketch the graph of this function. b) What is the only critical point of this function? Explain. c) Would the critical point change in any way if we would consider g(x) = 2|x| instead of f(x) = |x|? Explain why or why not. 3 3. Apply the Chain Rule and explain the differences among the following four ex- amples from the point of view of differentiation. Compute explicitly each one of the given derivatives: (cos(5z)) = Ccon(z")) = dr cos"(z) = and d (cos(sin(5æ))) = dz 4. Now, as explained in class, recall that some functions are defined implicitly by a relation between z and y such as r² + y² = 4. In such cases, differentiating with respect to a both sides helps us compute y'= 4. We should be careful, however, with the Chain Rule that needs to be applied in the way. That is, if y is assumed to be a function of æ, then (y²)' = 2y(y/') (e")' = (e")y/ and so on. This process is called impne amerenciationr
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning