I have little problem regarding the Find constants so that the directional derivative of $f(x,y,z) = axy^2+byz+cx^3z^2$ has maximum value $32$ in point $P$ given the direction .
In this problem there is no accept answer that is why I am asking As I think since maximum value is $32$ $|\nabla f(1,2,-1)|=\sqrt(2b-2c)^2=\pm (2b-2c)=32$
So we can get two answer
Is it correct?