Find the maximum rate of change

[andyk23]

Find the maximum rate of change of the function f(x,y) = (3 y^5)/x at the point (1,2)

First I took the gradient of f(x,y)=<-3y^5*x^-2,15y^4*x^-1>
and took the pt <1/sqrt(5),2/sqrt(5)>
Then <-3y^5*x^-2,15y^4*x^-1>*<1/sqrt(5),2/sqrt(5)>
the answer i get is 171.73
I'm not sure where my error is

 

[SammyS]

Find the maximum rate of change of the function f(x,y) = (3 y^5)/x at the point (1,2)

First I took the gradient of f(x,y)=<-3y^5*x^-2,15y^4*x^-1>
and took the pt <1/sqrt(5),2/sqrt(5)>
Then <-3y^5*x^-2,15y^4*x^-1>*<1/sqrt(5),2/sqrt(5)>
the answer i get is 171.73
I'm not sure where my error is

Why not evaluate the gradient at the point (1, 2) ?

 

[andyk23]

Sorry I evaluated at the gradient(1,2)=<-96,240> and then <-96,240>*<1/sqrt(5),2/sqrt(5)>