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MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021 MAC 2233 Homework 5 Spring 2021 Name___________________________________ Show all work in the space provided. If no work is shown, the problem will receive at most half credit for a correct answer. â– More Applications of 𒇠′(ð’™) and 𒇠′′(ð’™) to sketch the graph of ð’‡(ð’™) , also optimization problems for business • For problems 81) through 84), sketch the graph of a function ð‘“(ð‘¥) that has all the given properties 81) o ð‘“′(ð‘¥) > 0 ð‘¤â„Žð‘’ð‘› ð‘¥ < 0 ð‘Žð‘›ð‘‘ ð‘¤â„Žð‘’ð‘› ð‘¥ > 5 , o ð‘“′(ð‘¥) < 0 ð‘¤â„Žð‘’ð‘› 0 < ð‘¥ < 5, o 𑓠′′(ð‘¥) > 0 ð‘¤â„Žð‘’𑛠− 6 < ð‘¥ < −3 ð‘Žð‘›ð‘‘ ð‘¤â„Žð‘’ð‘› ð‘¥ > 2 , o 𑓠′′(ð‘¥) < 0 ð‘¤â„Žð‘’ð‘› ð‘¥ < −6 ð‘Žð‘›ð‘‘ ð‘¤â„Žð‘’𑛠− 3 < ð‘¥ < 2 .

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING ) o 𑓠′(ð‘¥) > 0 ð‘¤â„Žð‘’ð‘› ð‘¥ < −2 ð‘Žð‘›ð‘‘ ð‘¤â„Žð‘’𑛠− 2 < ð‘¥ < 3, o 𑓠′(ð‘¥) < 0 ð‘¤â„Žð‘’ð‘› ð‘¥ > 3, o 𑓠′(−2) = 0 and 𑓠′(3) = 0. MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING ) o ð‘“′(ð‘¥) > 0 ð‘¤â„Žð‘’ð‘› 1 < ð‘¥ < 2, o 𑓠′(ð‘¥) < 0 ð‘¤â„Žð‘’ð‘› ð‘¥ < 1 ð‘Žð‘›ð‘‘ ð‘¤â„Žð‘’ð‘› ð‘¥ > 2 , o 𑓠′′(ð‘¥) > 0 ð‘“ð‘œð‘Ÿ ð‘¥ < 2 ð‘Žð‘›ð‘‘ ð‘“ð‘œð‘Ÿ ð‘¥ > 2 , o 𑓠′(1) = 0 and 𑓠′(2) ð‘–ð‘ ð‘¢ð‘›ð‘‘ð‘’ð‘“ð‘–ð‘›ð‘’ð‘‘ MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING ) o ð‘“′(ð‘¥) > 0 ð‘¤â„Žð‘’ð‘› ð‘¥ < 1, o 𑓠′(ð‘¥) < 0 ð‘¤â„Žð‘’ð‘› ð‘¥ > 1 , o 𑓠′′(ð‘¥) > 0 ð‘¤â„Žð‘’ð‘› ð‘¥ < 1 ð‘Žð‘›ð‘‘ ð‘¤â„Žð‘’ð‘› ð‘¥ > 1 , o 𑓠′(1) ð‘–ð‘ ð‘¢ð‘›ð‘‘ð‘’ð‘“ð‘–ð‘›ð‘’ð‘‘.

MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING 2021 • For problems 85) through 88), find the Absolute-Maximum and the Absolute-Minimum values (if any) of the function ð‘“(ð‘¥) on the specified interval 85) ð‘“(ð‘¥) = −2ð‘¥ 3 + 3ð‘¥ 2 + 12𑥠− 5 ; ð‘œð‘› − 3 ≤ 𑥠≤ ) ð‘“(ð‘¥) = −3ð‘¥ 4 + 8ð‘¥ 3 − 10 ; ð‘œð‘› 0 ≤ 𑥠≤ 3 MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING ) ð‘“(ð‘¥) = ð‘¥2 ð‘¥+1 ; ð‘œð‘› − 1 2 ≤ 𑥠≤ ) ð‘“(ð‘¥) = 2ð‘¥ + 8 ð‘¥ + 2 ; ð‘œð‘› ð‘¥ > 0 MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING ) Find two positive numbers whose sum is 50 and whose product is as large as possible. 90) The are 320 yards of fencing available to enclose a rectangular field.

How should this fencing be used so that the enclosed area is as large as possible? MIAMI DADE COLLEGE PROFESSOR; RAYSURI A. ZAITER-CICCONE MAC 2233 SPRING ) Prove that of all rectangles with a given perimeter, the square has the largest-Area. 92) Prove that of all rectangles with a given area, the square has the Smallest-Perimeter. MIAMI DADE COLLEGE PROFESSOR; RAYSURI A.

ZAITER-CICCONE MAC 2233 SPRING ) A carpenter has been asked to build an open box with a square base. The sides of the box will cost