Let g(x) = x V 81 - x2. %D g'(x) = A+ Bx2 where (81 - x)c" B = Dx + Ex g"(x) = where %3D (81- xy" E = F =

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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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...
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Let g(x) = x V 81 – x².
A + Bx2
(81 - x2)c"
g'(x) =
where
A =
B =
C =
Dx3 + Ex
g"(x) =
where
(81 - xyF
D =
E =
F =
Find the relative maximum and relative minimum values of g. Also find all inflection points of the graph, the interval(s) on which the graph of g is concave downward. Enter the values of the
endpoints in the appropriate blanks and DNE in any empty answer blanks. Finally, sketch the graph of the function, following the directions above, and bring it to your discussion section the day this
assignment is due. (Hint: Note the domain of the function as you work the problem.)
Relative maximum values, with the x-values in increasing order:
Relative minimum values, with the x-values in increasing order:
The graph has inflection point(s) at: (x-values in increasing order)
The graph is concave downward on the following interval(s):
O (-0, 0)
O (-0, d)
Transcribed Image Text:Let g(x) = x V 81 – x². A + Bx2 (81 - x2)c" g'(x) = where A = B = C = Dx3 + Ex g"(x) = where (81 - xyF D = E = F = Find the relative maximum and relative minimum values of g. Also find all inflection points of the graph, the interval(s) on which the graph of g is concave downward. Enter the values of the endpoints in the appropriate blanks and DNE in any empty answer blanks. Finally, sketch the graph of the function, following the directions above, and bring it to your discussion section the day this assignment is due. (Hint: Note the domain of the function as you work the problem.) Relative maximum values, with the x-values in increasing order: Relative minimum values, with the x-values in increasing order: The graph has inflection point(s) at: (x-values in increasing order) The graph is concave downward on the following interval(s): O (-0, 0) O (-0, d)
The graph is concave downward on the following interval(s):
O (-∞, ∞)
O (-∞, d)
O (-0, d]
O (d, ∞)
O [d, ∞)
(-0, d) U (f, ∞)
O (-∞, d] U [f, 0)
O (-~, d) U (f, h)
O (d, f) U (h, ∞)
O (d, f)
O [d, f)
O None of the Above.
d =
f =
h =
symbolic formatting help
Transcribed Image Text:The graph is concave downward on the following interval(s): O (-∞, ∞) O (-∞, d) O (-0, d] O (d, ∞) O [d, ∞) (-0, d) U (f, ∞) O (-∞, d] U [f, 0) O (-~, d) U (f, h) O (d, f) U (h, ∞) O (d, f) O [d, f) O None of the Above. d = f = h = symbolic formatting help
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