Any hints
#how to do this
gaunt plinth
cobalt otterBOT
Any hints
- Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
- Wait patiently for a helper to come along.
- Once someone helps you, say thank you and close the thread with:
+close - Feel free to nominate the person for helper of the week in #helper-nominations
- Do not ping the mods, unless someone is breaking the rules.
- If you're happy with the help you got here, and the server overall, you can contribute financially as well:
fallen basalt
the plane is tangent to the surface, when does that happen?
the gradient is collinear with the normal of the plane, which is (1,2,3)
this implies x=z=-y at a touching point, now we can guess a touching point with the surface equation: x^2-2y^2+3z^2=2 for example we can take (x,y,z)=(1,-1,1), thus p = 1-2+3=2
@gaunt plinth
fallen basalt
to take your example even
the paraboloid z = x^2 + y^2
its tangent surface at (0,0) is simply the xy plane
the gradient at (0,0) is (0,0,-1)
@gaunt plinth
revise definitions
i think you are incorrectly applying your intuition about single variable derivatives to 3d space
e.g for y=x^2 the derivative at 0 is 0, but that's not gradient
the gradient is (0,-1)
which is again normal to the tangent line
gaunt plinth
this implies x=z=-y at a touching point, now we can guess a touching point with ...
x=z=-y?
How it came
Rest i understood
gaunt plinth
Ohh you compared both coefficients of plane and curve
1 1
2 -2
3 3
So it gives (1 -1 1)
fallen basalt
x=z=-y?
the normal of the plane is (1,2,3) where as the gradient of the surface is (2x,-2y,6z)
these vectors must be collinear
@gaunt plinth
fallen basalt
gaunt plinth
<:noway:1060890722657648680>
What happened?
You did mistake in derivative
2x-4y+6z
@fallen basalt
fallen basalt
this is a multivariable function
there is no "derivative"
you can speak of partial derivatives or total derivative
@gaunt plinth
gaunt plinth
Yeah
