Specific slope for directional derivative?

[glog]

Is there a direction where the rate of change is 18, at the point (-1,2) on the function f(x,y) = (x^2)(y^3)+xy?

So I found the gradient of this function, picked a random direction vector u = ( a / (a^2+b^2)^(1/2) , b / (a^2+b^2)^(1/2) ) and took the dot product, and set it to 18... however, I have one equation with two unknowns and no idea how to proceed.

Thank you.

 

[rootX]

Is there a direction where the rate of change is 18, at the point (-1,2) on the function f(x,y) = (x^2)(y^3)+xy?

So I found the gradient of this function, picked a random direction vector u = ( a / (a^2+b^2)^(1/2) , b / (a^2+b^2)^(1/2) ) and took the dot product, and set it to 18... however, I have one equation with two unknowns and no idea how to proceed.

Thank you.

don't do that mess..

just say u = <a,b> is unit vector
so, a^2+b^2 = 1 would be your second equation
and
<a,b>.del f = 18 your first equation

I found del f to be <-14,11>
this might be wrong, because I didn't recheck my work

 

[Defennder]

It doesn't matter if you have 2 unknowns. You're interested in the direction, not the magnitude of the direction vector. Express either a or b in terms of the other and then normalise the vector (a,b)