# San Joaquin Delta College Multivariable Breakout Room Problem Question

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Breakout Room Problem #5:
Problem #5 is not from your text but will allow me to see how you can put the concepts of
Chapter 13 together to solve this problem. This problem is ” similar to” what is
demonstrated in example #3 on page 896 of your text. Create the Calcplot3D images that
displays the following descriptions:
A point moves along the path of the curve which is the intersection of the surface z = x2 +47 and the
plane y = 1.
a) Find the slope of the tangent line at (-1, 1, 5).
b) Find the equation of the tangent line at (-1,1,5)
A point moves along the path of the curve which is the intersection of the surface z = x +472 and the
planex=-1.
C) Find the slope of the tangent line at (-1, 1, 5).
d) Find the equation of the tangent line at (-1,1,5)
el Use CalcPlot3D to graph the three surfaces, the two curves of intersection, respectively, and the two
tangent lines at (-1,1,5)
Explain and Deliver:
Before I could arrive at my solution, I had to…
Here are the calculations that are outlined in the
description of my process.
896
– yoo to
Chapter 13 Functions of Several Variables
EXAMPLE 3 Finding the Slopes of a Surface
i… See Larson Calculus.com for an interactive version of this type of example.
Find the slopes in the x-direction and in the y-direction of the surface
f(x, y) =
25
at the point (1, 1, 2).
Solution The partial derivatives of f with respect to x and y are
f(x, y) = -x and f(x, y) = -2y.
Partial derivatives
So, in the x-direction, the slope is
(51)
Figure 13.30
and in the y-direction, the slope is
(1) = -2
Figure 13.31
Surface:
f(x,y)=-
-y?
100
(6.1,2)
-(1,1,2)
Slope in x-direction:
(11) —
Slope in y-direction:
(-+) –2
Figure 13.30
Figure 13.31

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Tags:
partial derivatives

slope of the tangent

curve of intersection

slopes of surface

intersection of the surface

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