# Breakout Room Problem

+ 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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