following parts, sketch the graph of a continuous function on the grid at satisfies all of the given criteria. If no such functions exist, write 'DNE' with a brief explanation why the function does not exist in the space provided below. (a) A function p(r) with domain (0, 8) that has p'(x) > 0 everywhere, p"(x) = 0 for all r < 4, and p"(r) < 0 for all r> 4. (b) A function r(x) with domain [0, 8] that has a global maximum at r = 2 and a local max- imum at r = 8.
following parts, sketch the graph of a continuous function on the grid at satisfies all of the given criteria. If no such functions exist, write 'DNE' with a brief explanation why the function does not exist in the space provided below. (a) A function p(r) with domain (0, 8) that has p'(x) > 0 everywhere, p"(x) = 0 for all r < 4, and p"(r) < 0 for all r> 4. (b) A function r(x) with domain [0, 8] that has a global maximum at r = 2 and a local max- imum at r = 8.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![In each of the following parts, sketch the graph of a continuous function on the grid that
satisfies all of the given criteria. If no such functions exist, write 'DNE' with a brief explanation why
the function does not exist in the space provided below.
(a) A function p(x) with domain (0, 8) that has
p'(x) > 0 everywhere, p"(x) = 0 for all r <
4, and p"(x) < 0 for all æ > 4.
(b) A function r(x) with domain [0, 8] that has
a global maximum at r = 2 and a local max-
imum at r = 8.
6
-4
-4
(c) A function q(x) with domain (0,8) that sat-
isfies q (2) = -1, q'(6) = 0, and q" (r) < 0
everywhere.
(d) A function s(x) with domain (0, 8) that has
an inflection point at r = 4 and satisfies
s'(x) < 0 everywhere in its domain.
4
2
-2
-4
-4
2.
2.
6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7ed6912-b2c6-4065-b0eb-ce104ed6ab5a%2F6b91ca57-99f3-4491-ae72-dbf8b5abe7de%2Fz4fffci_processed.png&w=3840&q=75)
Transcribed Image Text:In each of the following parts, sketch the graph of a continuous function on the grid that
satisfies all of the given criteria. If no such functions exist, write 'DNE' with a brief explanation why
the function does not exist in the space provided below.
(a) A function p(x) with domain (0, 8) that has
p'(x) > 0 everywhere, p"(x) = 0 for all r <
4, and p"(x) < 0 for all æ > 4.
(b) A function r(x) with domain [0, 8] that has
a global maximum at r = 2 and a local max-
imum at r = 8.
6
-4
-4
(c) A function q(x) with domain (0,8) that sat-
isfies q (2) = -1, q'(6) = 0, and q" (r) < 0
everywhere.
(d) A function s(x) with domain (0, 8) that has
an inflection point at r = 4 and satisfies
s'(x) < 0 everywhere in its domain.
4
2
-2
-4
-4
2.
2.
6.
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