Question

Can somebody help me with Exam 2 problem 2? I have no idea where to start.

Answer 1

ok to start off it tells us we are on the level curve f=2000 so we are only on the portion of the graph labeled 2000. then it says partial f over partial y (sorry dont know how to do partial sign) is \[\ge 0\] which partial f over partial y is approximately change in f over change in y assuming x remains fixed. so that means that if f increases y must also increase and if f decreases y must also decrease. so in math terms \[\Delta f/\Delta y \ge 0 \rightarrow + \Delta f /(+\Delta y) or -\Delta f/(-\Delta y)\]
so you need to find points on the level curve f=2000 where if you move in the vertical direction both up and down it satisties the expression above.

Answer 2

if that still doesnt make sense let me know

Answer 3

Well from the very start I know to start at the 2000 mark. If you could explain it in a slightly different way maybe that would help more. Your explanation has set me on the right path but Im not quite at full comprehension yet. Thank you

Answer 4

so what i did is pick a point on the level curve and at the point go straight up. going up on the piece of paper means that we are increasing y so \[\Delta y\] is greater than 0 and if you go inbetween the level curve of 2000 and the next highest level curve then that means \[\Delta f \ge 0\] so you then have to find all the points where this is true...sorry its hard to explain without actually being able to point it out to you in person but this video the professor does explains a similar problem hopefully this helps its only the last 5 minutes of the video http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/exam-2/session-46-review-of-problems/

Answer 5

The lightbulb went off. Thank you, that was a perfect explanation