For each of the following functions, find all local maximum and mini- mum points. х, х# 3, 5, 7, 9 5, х 3D 3 –3, x = 5 9, x = 7 7, (i) f(x) = x = 9. | 0, x irrational 1/q, x = p/q in lowest terms. x rational 1 0, x irrational. | 1, x = 1/n for some n in N 0, otherwise. (ii) f(x) = х, (iii) f(x) (iv) f(x) 1, if the decimal expansion of x contains a 5 0, otherwise. (v) f(x)
For each of the following functions, find all local maximum and mini- mum points. х, х# 3, 5, 7, 9 5, х 3D 3 –3, x = 5 9, x = 7 7, (i) f(x) = x = 9. | 0, x irrational 1/q, x = p/q in lowest terms. x rational 1 0, x irrational. | 1, x = 1/n for some n in N 0, otherwise. (ii) f(x) = х, (iii) f(x) (iv) f(x) 1, if the decimal expansion of x contains a 5 0, otherwise. (v) f(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
Please solve question 5 completely
![8:37 AM Ø
VOLTE 4 28%
3
= x +
x?
(ii) f(x)
x?
(iii) f(x)
х2 — 1
1
(iv) f(x)
1 + x?
4.
(a) If a1 < · ·. = > (x – a;)?.
< an, find the minimum value of f(x)
*(b) Now find the minimum value of f(x) = ) ]* -
a;l. This is a prob-
lem where calculus won't help at all: on the intervals between the
a;'s the function f is linear, so that the minimum clearly occurs at one
of the a;, and these are precisely the points where f is not differ-
entiable. However, the answer is easy to find if you consider how
f(x) changes as you pass from one such interval to another.
*(c) Let a > 0. Show that the maximum value of
1
1
+
1 + |x|
f(x) =
1+ |x - al
is (2 + a)/(1 + a). (The derivative can be found on each of the
intervals (- o, 0), (0, a), and (a, o) separately.)
For each of the following functions, find all local maximum and mini-
mum points.
5.
x, x * 3, 5, 7, 9
5,
X = 3
-3, x = 5
9, x = 7
7, х 3D 9.
(i) f(x)
=
0,
1/g, x = p/g in lowest terms.
x rational
| 0, x irrational.
x irrational
(ii) f(x)
х,
(iii) f(x)
=
* = 1/n for some n in N
0, otherwise.
(iv) f(x)
1, if the decimal expansion of x contains a 5
0, otherwise.
(v) f(x)
6. (a) Let (x0, yo) be a point of the plane, and let L be the graph of the
function f(x) = mx + b. Find the point F such that the distance
from (xo, yo) to (x, f(x)) is smallest. [Notice that minimizing this
distance is the same as minimizing its square. This may simplify
the computations somewhat.]
Alee fo](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49e60f1d-a03d-4abd-b02e-d7681ad9c98e%2F3c1a2573-cb9b-4a99-8fa8-7dda9a02d247%2Fzkmvcjq_processed.png&w=3840&q=75)
Transcribed Image Text:8:37 AM Ø
VOLTE 4 28%
3
= x +
x?
(ii) f(x)
x?
(iii) f(x)
х2 — 1
1
(iv) f(x)
1 + x?
4.
(a) If a1 < · ·. = > (x – a;)?.
< an, find the minimum value of f(x)
*(b) Now find the minimum value of f(x) = ) ]* -
a;l. This is a prob-
lem where calculus won't help at all: on the intervals between the
a;'s the function f is linear, so that the minimum clearly occurs at one
of the a;, and these are precisely the points where f is not differ-
entiable. However, the answer is easy to find if you consider how
f(x) changes as you pass from one such interval to another.
*(c) Let a > 0. Show that the maximum value of
1
1
+
1 + |x|
f(x) =
1+ |x - al
is (2 + a)/(1 + a). (The derivative can be found on each of the
intervals (- o, 0), (0, a), and (a, o) separately.)
For each of the following functions, find all local maximum and mini-
mum points.
5.
x, x * 3, 5, 7, 9
5,
X = 3
-3, x = 5
9, x = 7
7, х 3D 9.
(i) f(x)
=
0,
1/g, x = p/g in lowest terms.
x rational
| 0, x irrational.
x irrational
(ii) f(x)
х,
(iii) f(x)
=
* = 1/n for some n in N
0, otherwise.
(iv) f(x)
1, if the decimal expansion of x contains a 5
0, otherwise.
(v) f(x)
6. (a) Let (x0, yo) be a point of the plane, and let L be the graph of the
function f(x) = mx + b. Find the point F such that the distance
from (xo, yo) to (x, f(x)) is smallest. [Notice that minimizing this
distance is the same as minimizing its square. This may simplify
the computations somewhat.]
Alee fo
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 4 steps with 4 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