Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (If an answer does not exist, enter DNE.) x=1-t , y=t^2

Horizontal tangent
(x, y)=
Vertical tangent
(x, y)=

Horizontal tangent

(x, y) = (1, 0)

Vertical tangent

(x, y) = DNE

Step-by-step explanation:

The equation for the slope (m) of the tangent line at any point of a parametric curve is:

Where and are the first derivatives of the horizontal and vertical components of the parametric curves. Now, the first derivatives are now obtained:

and

The equation of the slope is:

As resulting expression is a linear function, there are no discontinuities and for that reason there are no vertical tangents. However, there is one horizontal tangent, which is:

The point associated with the horizontal tangent is:

The answer is:

Horizontal tangent

(x, y) = (1, 0)

Vertical tangent

(x, y) = DNE

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:

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.