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!