Determine the five-point summary for the function f(x) = cos (2x + 3) + 5 using algebraic methods. Give all values in exact form (no decimal equivalents).
Determine the five-point summary for the function f(x) = cos (2x + 3) + 5 using algebraic methods. Give all values in exact form (no decimal equivalents).
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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Transcribed Image Text:Determine the five-point summary for the function f (x) = cos(2x + 3) + 5 using
algebraic methods. Give all values in exact form (no decimal equivalents).
![Determine the five-point summary for the
function f(x) = cos
algebraic methods.
cos
Step 2: Solution
The given function is
Let y = f(x)
3π
cos (2x + ³) +5
2
cos(0) always lies between [-1, 1]
So, cos(0) lies between [4, 6]
So, maximum values and minimum values of
the function f(x) is 6 and 4 respectively.
Now, put x= 0 in f(x), we get
y = cos (37) +5
y= 0+5=5
Now, put x =
f(x) = cos(+³7) +5
f(x) = cos (π) +5
f(x) = -1+5= 4
Now put x
y = f(x) =
COS
y = cos(2T) + 5
y=1+5= 6
=
(²/2+³/7) +5
Now, put x =
y = f(x)
y = f(x)
y = √2 +5
cos (+3)+5
cos (4) +5
Now, put x =
y = f(x)
y = f(x)
y=+5
=
ㅠ
ㅠ
2
, in f(x), we get
2
(2x + 3) + 5 using
in f(x), we get
we get
ㅠ
2
COS
s(-4+³/7) + 5
sin (-4) + 5 = sin (7) + 5
, we get
Solution
Hence, the five point summery is
(0, 5), (7, 4), (1, 6) (½, ½ + 5), (3, + 5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc7689b9-c4fe-4bee-b670-05d15f3915cb%2Fa252efed-c0ac-44e4-929b-45f181cf9209%2Fmv1a2g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine the five-point summary for the
function f(x) = cos
algebraic methods.
cos
Step 2: Solution
The given function is
Let y = f(x)
3π
cos (2x + ³) +5
2
cos(0) always lies between [-1, 1]
So, cos(0) lies between [4, 6]
So, maximum values and minimum values of
the function f(x) is 6 and 4 respectively.
Now, put x= 0 in f(x), we get
y = cos (37) +5
y= 0+5=5
Now, put x =
f(x) = cos(+³7) +5
f(x) = cos (π) +5
f(x) = -1+5= 4
Now put x
y = f(x) =
COS
y = cos(2T) + 5
y=1+5= 6
=
(²/2+³/7) +5
Now, put x =
y = f(x)
y = f(x)
y = √2 +5
cos (+3)+5
cos (4) +5
Now, put x =
y = f(x)
y = f(x)
y=+5
=
ㅠ
ㅠ
2
, in f(x), we get
2
(2x + 3) + 5 using
in f(x), we get
we get
ㅠ
2
COS
s(-4+³/7) + 5
sin (-4) + 5 = sin (7) + 5
, we get
Solution
Hence, the five point summery is
(0, 5), (7, 4), (1, 6) (½, ½ + 5), (3, + 5)
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