How Do You Determine Constants A, B, and C in the Function f(x, y, z)?

[ori]

the question
f(x,y,z)=Axy^2+Byz+Cx^3*z^2
given data: at point(1,2,-1) the maximum pointed devertive of f is
at direcation
x=0 y=0 z=1
and its value is 32
so what are they A,B ,C?

the only thing i know that since the func is differncial
32=(0,0,1)*grad f
and from here we get
B-C=16

but how do we get 2 more equation?
i don't know how to use the data that this is the max pointed devertive

 

[arildno]

Remember that the gradient must be parallell to the direction of maximal "pointed" derivative!
The gradient is therefore:
$$\nabla{f}=(0,0,32)$$
Hence, you get 3 equations with 3 unknowns, one equation for each component.

 

[ori]

Remember that the gradient must be parallell to the direction of maximal "pointed" derivative!
The gradient is therefore:
$$\nabla{f}=(0,0,32)$$
Hence, you get 3 equations with 3 unknowns, one equation for each component.

thank u
how did u do the formula? (with the grad symbol)

 

[HallsofIvy]

He used \nabla in a "tex" formula.

Click on any "tex" formula and you will see the code used.