(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

attached.

2. Relevant equations

3. The attempt at a solution

I thought the problem was easy, but my answer is wrong (aparently; I still disagree.)

First I defined x = (y^3)(z^3) to be a surface of function F

So

F(x,y,z) = (y^3)(z^3) - x = 0

Then, the gradient of F:

Partial wrt x = -1

Partial wrt y = 3y^2(z^3)

Partial wrt z = 3z^2(y^3)

Gradient F = -1i + 3y^2(z^3)j + 3z^2(y^3)k

Gradient F(1,-1,-1) = -1i + 3(-1)^2((-1)^3)j + 3(-1)^2((-1)^3)k

= -i - 3j - 3k

Then the tangent plane formula is

- x - 3y - 3z = 5

or

x + 3y + 3z = -5

Where am I going wrong with this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Calc III - finding tangent plane

**Physics Forums | Science Articles, Homework Help, Discussion**