Use the given parameters to answer the following questions. If you have a graphing device, graph the curve to check your work.x = 9 - t2y = t3 - 12t(a) Find the points on the curve where the tangent is horizontal.(b) Find the points on the curve where the tangent is vertical.

Question
Asked Nov 4, 2019
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Use the given parameters to answer the following questions. If you have a graphing device, graph the curve to check your work.
x = 9 - t2
y = t3 - 12t

(a) Find the points on the curve where the tangent is horizontal.

(b) Find the points on the curve where the tangent is vertical.

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Expert Answer

Step 1
It is given that, the two equations are x 9-2 andy = t -12t
dy
Obtain the value of m
dx
dy
dy dt
dx
dx
dt
d
(2-12t)
dt
d
(9-r)
dt
3t2 -12
-2t
3t2-12
Thus, the tangent line at a point t is m =
-2t
help_outline

Image Transcriptionclose

It is given that, the two equations are x 9-2 andy = t -12t dy Obtain the value of m dx dy dy dt dx dx dt d (2-12t) dt d (9-r) dt 3t2 -12 -2t 3t2-12 Thus, the tangent line at a point t is m = -2t

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Step 2
(a)
It is known that, the tangent is horizontal the slope is 0.
3t2 -12
0
-2t
t = +2
At t -2
x =9-(-2) and y-(-2-12(-2)
x 9-4 and y=-8+24
x 5 and y 16
help_outline

Image Transcriptionclose

(a) It is known that, the tangent is horizontal the slope is 0. 3t2 -12 0 -2t t = +2 At t -2 x =9-(-2) and y-(-2-12(-2) x 9-4 and y=-8+24 x 5 and y 16

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Step 3
At t 2
x9-(2) and y (2)-12(2)
x 9-4 andy= 8 - 24
x 5 and y16
Thus, the points on the curve where the tangent is horizontal are
(5,16) and (5,-16)
help_outline

Image Transcriptionclose

At t 2 x9-(2) and y (2)-12(2) x 9-4 andy= 8 - 24 x 5 and y16 Thus, the points on the curve where the tangent is horizontal are (5,16) and (5,-16)

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