The plane y=1 intersects the surface z=x5+2xy−y5 in a certain curve. Find the slope of the tangent line of this curve at the point P=(1,1,2).

slope = 7

Step-by-step explanation:

You have that the plane y=1 intersects the following surface:

            (1)

To find the slope of the curve, you first replace y=1 in the equation (1):

      (2)

This is the generated curve when the plane y=1 intersect the surface z.

The slope of a function is given by the derivative of the function. Then, you calculate dz/dx in the equation (2):

The slope only depends of the value of x. The slope for the point P(1,1,2) is:

The value of the slope of the tangent line to point P is 7

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation:

step-by-step explanation:

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