Question

Find an equation for the tangent plane at the point P: x^2 + 5yz. P = (1,2,19/10)

Answer 1

the derivative of a plane is the equation for the normal

Answer 2

Dx = 2x
Dy = 5z
Dz = 5y

the normal to the tangent plane at the point is: <2x,5z,5y>

Answer 3

<2(1),5(19/10),5(2)>

<2,19/2,10>, or simply the normal is <4,19,10>

Answer 4

and just apply it to the point given:

4(x-1)+19(y-2)+10(z-19/10) = 0

Answer 5

http://www.wolframalpha.com/input/?i=+plot+x^2+%2B+5yz
now that is a surface :)

Answer 6

Ahhh, I see what to do for that. Thanks! :)

Answer 7

http://www.wolframalpha.com/input/?i=+plot++4%28x-1%29%2B19%28y-2%29%2B10%28z-19%2F10%29%3D0%2Cx^2%2B5yz%2C

youre welcome

Answer 8

Oh wait a minute, sorry I forgot to add this:
x^2 + 5yz = 20

Sorry about that

Answer 9

I forgot to put the = 20