3. Suppose that f(x)=2000x-.02.r³+6²-2216r-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) = = 2000.062² +1222-2216 f" (re) = =-1122 +12 1 Domain and range are both R. So, look for optimia where t"=0 -106x² +12x-216 x f'(x) f(x) 19 -4.83 20 0 21 4.77 179 180 ~-0326² +62-108 = 0 This quadratic bas 2 solutir 3 181 4.77 3 0 -4.83) f"2₂0 when x2 = 100 4.8 -4.8 x=20 x=180 f" (99) f¹ (101) = 191.97 = 191-97 => point of in flechon First derivatie test f' No change in sign of slope. 1 gues from at x = 20 = min. If' дос from so 22150 =) такій Second derivatreted. to so at I f" (20) >0 =) min. | f" (180) <0 =) maximu fix) 2 -216 20 180
3. Suppose that f(x)=2000x-.02.r³+6²-2216r-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) = = 2000.062² +1222-2216 f" (re) = =-1122 +12 1 Domain and range are both R. So, look for optimia where t"=0 -106x² +12x-216 x f'(x) f(x) 19 -4.83 20 0 21 4.77 179 180 ~-0326² +62-108 = 0 This quadratic bas 2 solutir 3 181 4.77 3 0 -4.83) f"2₂0 when x2 = 100 4.8 -4.8 x=20 x=180 f" (99) f¹ (101) = 191.97 = 191-97 => point of in flechon First derivatie test f' No change in sign of slope. 1 gues from at x = 20 = min. If' дос from so 22150 =) такій Second derivatreted. to so at I f" (20) >0 =) min. | f" (180) <0 =) maximu fix) 2 -216 20 180
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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can you please go over only the highlighted parts of the image. For example how did they get x= 20 and x= 180 for the first highlighted part?
Transcribed Image Text:3. Suppose that f(c) 2000 - .02³ +6²-2216r-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.
1
f'(x) =
f"(x)
= 2000.062² + 1224 -2216
=-1122 +12
Domain and range are
both R.
So, look for optimia where t'=0
-106x² +12x - 216
~-0326² +62-108 = 0
This quadratic bas 2 solution
179
180
181
x f'(x) f(x)
19
20
21
-4.83
0
4.77
4.77
D
4.8
1)
- 4.8.
-4.83
f"20 when x2 = 100
f" (99)
f¹ (101) = 191197
x=20
x=180
4
= 191-97 => point of
in flection
= 0
First derivatie text
f'
No change in
sign of slope.
1
goes from <o to >
at x = 20 =) min
I f'
3
дос
from
১০
2 2150 =) такій
desivätheted.
f" (20) >0 =) min.
I f" (180) <0 =) maxim.
f(x)
2
Second
-216
to co at
20
180
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