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A graph with tangent plane

mark

(10 pts)

For this problem, you’re going to plot the graph of a function of two variables together with the plane that’s tangent to the graph at the point (1,1). To get your function, choose your name from the following list:

mparog

My assigned function at point (1,1):

f(x,y) = 0.5x^2+0.6x^4

The tangent plane is:

L(x,y) = 1.1 + 3.4(x-1)

The graph is as follows:

rstahles

My assigned function of two variables is shown below:

f(x,y) = 1.8x^4 + 1.6x^2

The plane that’s tangent to this function at the point (1,1) is:

L(x,y) = 3.4 + 10.4(x-1)

The graph should look like this:

Here’s a link to the GeoGebra file that generated the image above.

dyost

My assigned function is:

f(x,y)=1.4x^4+1.2y^2

The equation for the plane tangent to the point (1,1) is:

L(x,y)=2.6+5.6(x-1)+2.4(y-1)

The graph looks like this:

whardin3

My assigned function is:

f(x,y)= 0.5x^4 + 0.5y^4

The tangent plane is:

L(x,y)= 1.0 + 2.0(x-1) + 2.0(y-1)

impish_wyvern

My assigned function at point (1,1) is f(x,y)=1.7x^4 +1.1y^4.

The equation of the tangent plane is L(x,y) = 2.8 + 6.8(x-1)+4.4(y-1).

Below is my graph:

ScottLashley

My assigned function of two variables is: f(x,y) = -(1.2x^4+y^4)

My tangent plane at the point (1,1) is: z=-4.8x-4y+6.6

Colby_Howell

My two variable function is:

f(x,y) = 0.9x^4+1.5y^2

The tangent plane of this function at point (1,1) is:

L(x,y) = 2.4+3.6(x-1)+3(y-1)

Their graph would look something like this:

Samwise

My assigned function was
f(x,y) = -(0.4x^2+1.4y^4).
The tangent plane at point (1,1) is equal to
L(x,y)= -1.8-0.8(x-1)-5.6(y-1).
The graph looks like this:

mbanawan

My assigned function is:
f(x,y) = 0.9x^4 + 1.4y^2
The equation of the tangent plane at point (1,1) is:
L(x,y) = 2.3 + 3.6(x-1) + 2.8(y-1)

Image of the graphs of f(x,y) and L(x,y):

Alexander_The_OK

with the equation f(x,y)=-6(x-\frac{1}{2})-4(y-\frac{1}{1.5}) there wasn’t a point where it touched at 1/1. I think I might have messed this up slightly, but it looks right.

mearing

My assigned function is:

f(x,y)=1.4x^2+y^2

Plane tangent at (1,1):

L(x,y)=2.4+2.8(x-1)+2(y-1)

myost

my assigned function is:

f(x,y) = -(0.8x^4+0.4y^2)

the tangent plane at point (1,1) is:

L(x,y) = -1.2-3.2(x-1)-0.8(y-1)

graph:

mhernan5

My function of two variables in shown below:
f(x,y)=1.7x^2+y^4
The equation for the plane tangent to the point (1,1) is:
L(x,y)=2.7+3.4(x-1)+4(y-1)
The graph looks like this: