find the tangent of the graph f(x,y)=6x-3x^2-y^2 at th point (1,2,-1).how ?pls help

Question

amistre64 · Answer

youll need to take the derivative;  and is that a tangent plane?  or tangent line?

anonymous · Answer

tANGENT PLANE

amistre64 · Answer

find the gradient sounds familiar then

amistre64 · Answer

the gradient produces a normal vector at a given point ...

anonymous · Answer

but how i can take derivatives of z co ordinate?

amistre64 · Answer

z = f(x,y)=6x-3x^2-y^2

f(x,y,z)=6x-3x^2-y^2-z

now the partials form the gradient;  (Fx, Fy, Fz)

amistre64 · Answer

Fx = 6-6x
Fy = -2y
Fz = -1


at the point (1,2,-1) we get Fx = 0
                                         Fy = -4
                                         Fz = -1

anonymous · Answer

i can do the rest but the prblem is how does f(x,y,z)=the equation happen?

amistre64 · Answer

recall how  y = f(x)  earlier in the courses?

amistre64 · Answer

the usual notation in 3d space is:  z is a function of x and y,  z = f(x,y)

anonymous · Answer

ok thnx a lot

amistre64 · Answer

youre welcome