3. Suppose that f(x) = 2000 2000.02³ +6²-2216.r 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) f²(x) = -₁122 + 12 2 = 2000.062 +1224 -2216 Domain and range are both R. So, look for optimia where t"=0 -1062² +12x - 216 --032² +62 - 108 = This quadratic bos 2 soluti x=20 = 0 - x -180 3

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for the highlighted part where did they get x= 20 and x=180 from?

3. Suppose that f(x): = 2000. - .02.2 + 6x²
.02.³ +6²-2216.r 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) = 2000.062 +1224 -2216
f"(x)
-1122 +12
2
Domain and range are
both R.
So, lok for optimia where t"=0
-1062² +12x - 216 = 0
--03x² +62 - 108 =
This quadratic bas 2 solution.
2
x=20
x=180
-] ³
3
Transcribed Image Text:3. Suppose that f(x): = 2000. - .02.2 + 6x² .02.³ +6²-2216.r 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) = 2000.062 +1224 -2216 f"(x) -1122 +12 2 Domain and range are both R. So, lok for optimia where t"=0 -1062² +12x - 216 = 0 --03x² +62 - 108 = This quadratic bas 2 solution. 2 x=20 x=180 -] ³ 3
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