# maximum rate of incerase

• Feb 27th 2010, 03:45 AM
alexandrabel90
maximum rate of incerase
give that f(x,y) = 5-x^2 -2y^2 and (x', y') = (-1,-1), the direction of the max rate of increase is

a. (2,4)
b. (1,2)
c. (1/5)^(1/2) (1,2)

isit all or just one of the above?

i thought the answer should be a. but my notes stats that it is c.

may i also know what formula i should used to get the direction that is gving zero rate of increase?
my working:

this direction would be perpendicular to grad f(x',y') hence we are looking for the tangent vertor which is the directional derivative at (x', y'), and that is equal to 2(5)^(1/2)

however my answers showed that the answer is plus minus (1/5)^(1/) (2, -1)

may i know what is wrong with my understanding please?

thanks!
• Feb 27th 2010, 03:56 AM
HallsofIvy
Quote:

Originally Posted by alexandrabel90
give that f(x,y) = 5-x^2 -2y^2 and (x', y') = (-1,-1), the direction of the max rate of increase is

a. (2,4)
b. (1,2)
c. (1/5)^(1/2) (1,2)

is it all or just one of the above?

Those are all vectors pointing in the same direction! They are all correct answers.
• Feb 27th 2010, 04:11 AM
alexandrabel90
may i know how part c is derived? i understand why part a and b could be the answers but not part c.

does that mean that eg (1/8)(1,2) can also be the answer since the direction of this vector is (1,2)?

thank you!