5. Consider the function f(x)=x² +ln x². [Hint: The domain of this function is all real numbers except 0.] Use calculus to determine where the graph of the function is concave upward and where it is concave downward (use interval notation to state your answers). Then determine inflection points, if any (express your answers as ordered pairs).
5. Consider the function f(x)=x² +ln x². [Hint: The domain of this function is all real numbers except 0.] Use calculus to determine where the graph of the function is concave upward and where it is concave downward (use interval notation to state your answers). Then determine inflection points, if any (express your answers as ordered pairs).
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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![5. Consider the function f(x)=x² +ln x² . [Hint: The domain of this function is all real numbers except 0.]
Use calculus to determine where the graph of the function is concave upward and where it is concave
downward (use interval notation to state your answers). Then determine inflection points, if any (express
your answers as ordered pairs).
f'G) = dx +
2
f
ş" (x ); [x .(4x)] - cdad ra2)
4x2 -2x² -2
(x) =
0 = (x) , f
4x&- dx?-2=0
" (oc) =
INE
ff
--
0 V2
(2x -) ( 2x t2) = Ò
20x - 1-0
dx t d=0
X = - 1
- 2
2
(+) / (+) = +
a 0,7305
2
ל (-!4 +'0)
%3D
Concave up:
(- ∞, O)
0)
0,7305
Concave down:
Inflection point(s):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F096386ee-a7d8-4324-afae-9f4cb3fd0785%2F4ea0b030-82c7-4f1e-b493-49dd95324c79%2Fehfuawl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Consider the function f(x)=x² +ln x² . [Hint: The domain of this function is all real numbers except 0.]
Use calculus to determine where the graph of the function is concave upward and where it is concave
downward (use interval notation to state your answers). Then determine inflection points, if any (express
your answers as ordered pairs).
f'G) = dx +
2
f
ş" (x ); [x .(4x)] - cdad ra2)
4x2 -2x² -2
(x) =
0 = (x) , f
4x&- dx?-2=0
" (oc) =
INE
ff
--
0 V2
(2x -) ( 2x t2) = Ò
20x - 1-0
dx t d=0
X = - 1
- 2
2
(+) / (+) = +
a 0,7305
2
ל (-!4 +'0)
%3D
Concave up:
(- ∞, O)
0)
0,7305
Concave down:
Inflection point(s):
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