MATH-M 311 Lecture 17: 14.8 Notes (Nov. 6)

• School: IU
• Department: Mathematics
• Course: MATH-M 311
• Professor: Bhaskar Siddharth

Document Summary

General format: given, find max/min values of on surface where. In case where : want to extrema of on some level curve o. For each value of , gradient vectors are as shown. Going along curve , increases from 1 to 4 and then decreases. At , there is a point at maximum of this region of where both gradients point in same direction. To solve for point where , if and given explicitly: At , tangent line to is parallel to that of , so it is also tangent to. So and are parallel: - they are scalar multiples of each other: proof: Maximizing/minimizing on can be done my maximizing/minimizing and plugging the resulting values into. Hence, is not a local max or min for along. Equivalently, not parallel to: conclusion: when achieves local max/min on level curve , at those points,