Question 24 In Problems 17 to 20, use the closed interval method to34. A close relative of the codling moth is the pea moth,Cydia nigricana, which is a pest of cultivated andgarden peas in several European countries. If itssearch period in one of the regions where it is a pestis given by the functionfind the global extrema on the indicated intervals.17. f(x) = x² – 4x + 2 on [0, 3]18. f(x) = x³ – 12x + 2 on [–3, 3]119. f(x) — х + — on [0.1, 10]1s(T) =for 20 < T < 30,-0.04T2 +27T – 1520. f(x) = xe¯* on [0, 100]then graph s(T) using information about the firstderivative over the domain 20 < T < 30. Be surethat your graph indicates the largest and smallestvalue of s over this interval.In Problems 21 to 24, use the open interval method tofind the global extrema on the indicated intervals.35. In Problem 30 of Problem Set 4.1, we saw that theweekly mortality rate during the outbreak of theplague in Bombay (1905–1906) can be reasonablywell described by the function21. f(x) = x² – 4x + 2 on (–∞, ∞)22. f(x) — х3 - 12х + 2 on (0, )123. f(x)= x + – on (0, ∞)f(t) = 890 sech²(0.2t – 3.4) deaths/weekX-24. f(x) = xe-* on (-where t is measured in weeks. Find the global maxi-mum of this function. Recall that25. Let f be continuous on the half-open interval [a, b)with b possibly equal to +o. Devise a method tofind the global extrema of f on this interval.2sech x =et + e-x26. Let f be continuous on the half-open interval (a, b]with a possibly equal to -o. Devise a method tofind the global extrema of f on this interval.36. Some species of plants (e.g., bamboo) flower onceand then die. A well-known formula for the averagegrowth rate r of a semelparous species (a species thatbreeds only once) that breeds at age x isIn[s(x)n(x)p]In Problems 27 to 30, use the half-open interval methodsyou developed in Problems 25 and 26 to find the globalextrema on the indicated intervals.r(x) =where s(x) represents the proportion of plantsthat survive from germination to age x, n(x) is thenumber of seeds produced at age x, and p is theproportion of seeds that germinate.27. f(x) = x² – 4x + 2 on [0, ∞)-28. f(x) = x³ – 12x + 2 on[1, 10)

24. The given function is: fx=xe-x on -∞,∞ To find the extrema on the indicated intervals.

In Problems 17 to 20, use the closed interval method to 34. A close relative of the codling moth is the pea moth, Cydia nigricana, which is a pest of cultivated and garden peas in several European countries. If its search period in one of the regions where it is a pest is given by the function find the global extrema on the indicated intervals. 17. f(x) = x2 - 4x + 2 on [0, 3] 18. f(x) = x3 - 12x +2 on [-3, 3] 1 19. f(x) = x +- on [0.1, 10] 1 s(T) = for 20 < T < 30, -0.0472 + 27 – 15 20. f(x) = xe- on [0, 100] then graph s(T) using information about the first derivative over the domain 20 < T < 30. Be sure that your graph indicates the largest and smallest value of s over this interval. In Problems 21 to 24, use the open interval method to find the global extrema on the indicated intervals. 35. In Problem 30 of Problem Set 4.1, we saw that the weekly mortality rate during the outbreak of the plague in Bombay (1905-1906) can be reasonably well described by the function 21. f(x) = x2 – 4x + 2 on (-o, 0) 22. f(x) = x³ - 12x +2 on (0, ox) 23. f(x)=x+ 1 on (0, o0) f(t) = 890 sech (0.2t – 3.4) deaths/week 24. f(x) = xe on (-oo, o) where t is measured in weeks. Find the global maxi- mum of this function. Recall that 25. Let f be continuous on the half-open interval [a, b) with b possibly equal to +oo. Devise a method to find the global extrema of f on this interval. 2 sech x = ex + e-x 36. Some species of plants (e.g., bamboo) flower once and then die. A well-known formula for the average 26. Let f be continuous on the half-open interval (a, b] with a possibly equal to -oo. Devise a method to find the global extrema of f on this interval. growth rate r of a semelparous species (a species that breeds only once) that breeds at age x is In[s(x)n(x)p] = (x). In Problems 27 to 30, use the half-open interval methods you developed in Problems 25 and 26 to find the global extrema on the indicated intervals. where s(x) represents the proportion of plants that survive from germination to age x, n(x) is the number of seeds produced at age x, and p is the proportion of seeds that germinate. 27. f(x) = x2 - 4x + 2 on [0, ox) 28. f(x) = x³ – 12x +2 on [1, 10)