MATH 140 Lecture 21: Applications

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Gulick

Document Summary

Math140 lecture 21 applications of max-min theorems. If c is the only critical number for f and if f(c) is a relative extreme, then it is an absolute extreme: do not forget about domain and units. Also, state what you are to find and label your answer: draw a picture, when relevant. Find the minimum length l of fencing if the field is to be totally enclosed, and the fence is to subdivide the field into two equal rectangular regions: picture, solution, minimize l. (cid:1876)(cid:2870)+(cid:4672) (cid:2869)(cid:2870)(cid:1876)+(cid:883)(cid:4673)(cid:2870: (cid:4666)(cid:1876)(cid:4667)= (cid:2870) (cid:3121)(cid:3120)(cid:3051)(cid:3118) (cid:3051)+(cid:2869)(cid:4672)(cid:2873)(cid:2870)(cid:1876) (cid:883)(cid:4673)=(cid:882) (cid:2873)(cid:2870)(cid:1876) (cid:883)=(cid:882) (cid:1876)=(cid:2870)(cid:2873) (cid:2869, (cid:4666)(cid:882)(cid:4667)=(cid:883),(cid:4666)(cid:884)(cid:4667)=(cid:884),(cid:4672)(cid:2870)(cid:2873)(cid:4673)=(cid:2870)(cid:2873) (cid:887, recall that =(cid:1874) (cid:1846), (cid:1846)=(cid:1846)(cid:2869)+(cid:1846)(cid:2870)= (cid:3051)(cid:3118)+(cid:2872)(cid:2871) +(cid:2873) (cid:3051)(cid:2872) ,(cid:882) (cid:1876) (cid:887, (cid:1846) (cid:4666)(cid:1876)(cid:4667)= (cid:3051)(cid:2871) (cid:3051)(cid:3118)+(cid:2872) (cid:2869)(cid:2872)=(cid:882) (cid:1858) (cid:3051)(cid:2871) (cid:3051)(cid:3118)+(cid:2872)=(cid:2869)(cid:2872) (cid:886)(cid:1876)=(cid:885) (cid:1876)(cid:2870)+(cid:886) (cid:1876)= (cid:2874) (cid:2875, a person in the woods is 2 miles from a road, and a restaurant is 5 miles down the road. The person can walk through the woods at 3 mph, and on the road a 4 mph.