You arc given the parametric equations x = 10 - t2, y = t3 - 12t. List all of th

Question

You arc given the parametric equations x = 10 - t2, y = t3 - 12t. List all of the points (x. y) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of X. If two or more points share the same value of X, list those points starting with the smallest value of y. If any blanks arc unused, type an upper-case "N" in them. Point 1: (x,y) = Point 2: (x, y) = Point 3: (x, y) = List all of the points (x. y) where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of X. If two or more points share the same value of J", list those points starting with the smallest value of y. If any blanks arc unused, type an upper-case "N" in them. Point 1 :{x,y) = Point 2: {x, y) = Point 3: (x, y) =

Explanation / Answer

x = 10 -t^2

y = t^3 -12t

tangent line is horizontal when dy/dt = 0

thus

3t^2 - 12 = 0

t^2-4 = 0
t= 2, -2

now

at t = 2

x = 10 -4 = 6

y = 2^3-12*2 = 8-24 = -16

at t = -2

x = 10-4 = 6

y = -8 + 12*2 = 24- 8 = 16

points are

(6,-16)
(6,16)
(N,N)

now

tangent line is vertical when dx/dt= 0 thus

-2t = 0

t = 0

thus

at t = 0

x = 10-0 = 10
y = 0-0   0

points are

(10, 0)
(N,N)
(N,N)

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