Common man, you have to show some effort, that's the way it works around here.
I have notes and can kinda figure out some of these problems but can't figure them out completely. Please show you work, and if you can please explain your steps.
1.) find the directional derivative of f(x,y) = sin(x+2y) at (4,2) in the direction of g = (3π/4)
2.) find the directional derivative of f(x,y,z) = z^(3) - x^(2) y at (1,6,2) in the direction of v = 3i + 4j + 12k
3.) find the maximum rate of change of f(x,y,z) = x^(2) y^(3) z^(4) at (1,1,1) and the direction in which it occurs.
4.) Find the relative maximum and/or minimum and/or saddle points of f(x,y) = 2xy - (1/2)(x^(4) + y^(4)) + 1
5.) find the symmetric equations of tangent line to the curve of intersection of the surfaces at the indicated point, and find the cosine of the angle between the gradient vectors at this point:
z = sqrt(x^(2) + y^(2)) , 5x - 2y + 3z = 22, (3,4,5)
6.) find the relative maximum and/or minimum and/or saddle points of f(x,y) = 120x + 120y - xy - x^(2) - y^(2)
7.) find the dimensions of the rectangular box with largest volume if the total surface area is given as 62 m^(2)
First: These are homework problems. Do NOT give full answers. Feel free to give hints but the OP needs to work these out on his/her own. Check forum rule #5 in the link in my signature.
Second:
mrb165: Let's let this thread answer the first three questions and repost the others in a new thread. This many questions in one thread is going to be horribly confusing.
-Dan