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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 8CR
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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?
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