Calculus Question!!

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zelda12

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f(x,y)=3xy^2-x-y
a) find the equation of the tangent place to the graph of f(x,y) at the point (2,1,3)

b) use the linear approximation to estimate the value of f(2.1,0.9)

c) find the directional derivative of f at (2,1) in the direction of i+j
 
I was able to get the normal vector of <2,11,0>, but now I am stuck and am not sure if that is even right..
 
zelda12 said:
I was able to get the normal vector of <2,11,0>, but now I am stuck and am not sure if that is even right..
Click to expand...
Please show us how you calculated the normal vector of the tangent plane - numerically and in detail.
 
zelda12 said:
f(x,y)=3xy^2-x-y
a) find the equation of the tangent place to the graph of f(x,y) at the point (2,1,3)

b) use the linear approximation to estimate the value of f(2.1,0.9)

c) find the directional derivative of f at (2,1) in the direction of i+j
Click to expand...
Did you learn about the equation of the tangent plane to a surface?
 
zelda12 said:
I remember apply it in a 2d space, but dont knoww how to apply it in a 3d space
Click to expand...

Calculus III - Tangent Planes and Linear Approximations

In this section formally define just what a tangent plane to a surface is and how we use partial derivatives to find the equations of tangent planes to surfaces that can be written as z=f(x,y). We will also see how tangent planes can be thought of as a linear approximation to the surface at a...
tutorial.math.lamar.edu
Please study the link above and see if you can apply it to your problem.
 
okay thank you!! So I feel good about the tangant plane, I got 12=2x+11y-z, and the approximation i got 2.1!!

I am still stuck on the direction derivative and its notation..
 
zelda12 said:
okay thank you!! So I feel good about the tangant plane, I got 12=2x+11y-z, and the approximation i got 2.1!!

I am still stuck on the direction derivative and its notation..
Click to expand...
Subhotosh Khan said:
Please show us how you calculated the normal vector of the tangent plane - numerically and in detail.
Click to expand...
Please share your work in detail. We can guide you to the answer of "directional derivative" from there.
 
Here's another link for directional derivative:

Calculus III - Directional Derivatives

In the section we introduce the concept of directional derivatives. With directional derivatives we can now ask how a function is changing if we allow all the independent variables to change rather than holding all but one constant as we had to do with partial derivatives. In addition, we will...
tutorial.math.lamar.edu
 
zelda12 said:
okay thank you!! So I feel good about the tangant plane, I got 12=2x+11y-z, and the approximation i got 2.1!!

I am still stuck on the direction derivative and its notation..
Click to expand...
Personally I don't feel too good about your equation for the tangent plane. Which means that one of us got it wrong. Do you want to share your work on this one?
 
blamocur said:
Formally speaking, "one of us" does not necessarily mean "only one of us", does it?;) But in this particular case I believe @zelda12 -- as well as @BigBeachBananas -- got it right.
Click to expand...

Yes, it means "only" one of you. It is necessarily singular. If you mean possibly more than one, you can state, "at least one."

Example: "One of us will do it." Both of you will not do it.
Example: "Give it to one of us." It will not be given to both of you.
 
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