Question

Give the unit vector that has the direction of maximum increase of the function .
f(x, y) at the location (−2, 1). For f(x,y)=x^2+2y^2-y

Answer 1

plug in x and y

Answer 2

f(-2,1)=(-2)^2+2*1^2-1

Answer 3

you will need the gradient first I think

Answer 4

Yeah is the answer not the gradient divided by the mag?

Answer 5

to get the unit vector? Since the max increase is in the same direction as the gradient?

Answer 6

yes, it should be gradient divided by magnitude

Answer 7

well, the gradient is the maximum direction of change; could be increase or decrease

Answer 8

so how do you know if it's increase or decrease?

Answer 9

I'm actually not too sure in this case. You could do it with multivariable max/min techniques if you know them.

Answer 10

alright man thanks for your help much appreciated

Answer 11

welcome