Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin , [0, 81]

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.4: Composition Of Functions
Problem 2SE: What is the composition of two functions, fg ?
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Find the point of inflection and discuss the concavity of the graph of the function.
f(x) = sin ,
[0, 81]
Transcribed Image Text:Find the point of inflection and discuss the concavity of the graph of the function. f(x) = sin , [0, 81]
Now, let f"(x) = 0 and solve for x. Remember that f"(x) = –
1
sin is a periodic function, and thus
16
4
there are infinitely many angles that satisfy the condition. For this step, just give the three angles when
0 < x< 8T. (Enter your answers as a comma-separated list.)
1
in 승 =
= 0
16
sin
= 0
4
= sin-1(0) + tn (where n is an integer)
4
X =
Out of those three values, only x =
is inside the open interval (0, 8t). We discard the
others, because concavity cannot change at the terminal point of the domain of a function.
Transcribed Image Text:Now, let f"(x) = 0 and solve for x. Remember that f"(x) = – 1 sin is a periodic function, and thus 16 4 there are infinitely many angles that satisfy the condition. For this step, just give the three angles when 0 < x< 8T. (Enter your answers as a comma-separated list.) 1 in 승 = = 0 16 sin = 0 4 = sin-1(0) + tn (where n is an integer) 4 X = Out of those three values, only x = is inside the open interval (0, 8t). We discard the others, because concavity cannot change at the terminal point of the domain of a function.
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