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!