3. Suppose that f(x) = 2000r.02.³+6²-2216.1920. Find all local and global maxima and minima of this function using the first and second derivative tests for maxima and minima. Plot the function. Is there a point of inflection? If so identify it and verify using the first derivative test.
3. Suppose that f(x) = 2000r.02.³+6²-2216.1920. Find all local and global maxima and minima of this function using the first and second derivative tests for maxima and minima. Plot the function. Is there a point of inflection? If so identify it and verify using the first derivative test.
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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![3. Suppose that f(c) 2000 - .02. +6²-2216.1920. Find all
local and global maxima and minima of this function using the first
and second derivative tests for maxima and minima. Plot the function.
Is there a point of inflection? If so identify it and verify using the first
derivative test.
f'(x)
f"(x)= = -₁122 +12
Domain and range are both R.
So, look for optimia where t"=0
-1062² +12x - 216 = 0
--0326² +6x2 - 108 = 0
This quadratic bos 2 soluti
27 to
x f'(x)] ƒ²(x)
19 -4.83
O
4.77
21
179
= 2000.0620² + (224-2216
180
181
4.77
D
-4.83/
f"20 when x = 100
4.8
- 4.8.
x=20
x=180
f" (99)
f² (101) = 191.97
4
= 191-97 => point of
in flection
[4] =
3
First derivate test
fi
No change in
sign of slope.
1
ques
at x = 20 =) min
If'
from <o to >
дов
from so
22150 =) такін
Second desivätreted.
-21.6
to so at
I f" (20) >0 =) min.
( f"l (180) <о =) тахіли
2
20
1
180](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba7d748a-252c-474b-931e-93acb5db0c03%2Fb549fcf7-754d-496e-ac89-ad03500cf870%2Fphxu9p_processed.png&w=3840&q=75)
Transcribed Image Text:3. Suppose that f(c) 2000 - .02. +6²-2216.1920. Find all
local and global maxima and minima of this function using the first
and second derivative tests for maxima and minima. Plot the function.
Is there a point of inflection? If so identify it and verify using the first
derivative test.
f'(x)
f"(x)= = -₁122 +12
Domain and range are both R.
So, look for optimia where t"=0
-1062² +12x - 216 = 0
--0326² +6x2 - 108 = 0
This quadratic bos 2 soluti
27 to
x f'(x)] ƒ²(x)
19 -4.83
O
4.77
21
179
= 2000.0620² + (224-2216
180
181
4.77
D
-4.83/
f"20 when x = 100
4.8
- 4.8.
x=20
x=180
f" (99)
f² (101) = 191.97
4
= 191-97 => point of
in flection
[4] =
3
First derivate test
fi
No change in
sign of slope.
1
ques
at x = 20 =) min
If'
from <o to >
дов
from so
22150 =) такін
Second desivätreted.
-21.6
to so at
I f" (20) >0 =) min.
( f"l (180) <о =) тахіли
2
20
1
180
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