I manage to get every answer, but the last one. Can somebody please check where

Question

I manage to get every answer, but the last one. Can somebody please check where I am going wrong. please and thank you!

(1 point) Consider the parametric curve: z=64-t2 At which t value(s) is the tangent to this curve vertical? (Note: if there is more than one write them as a comma separated list) 0) Write the point(s) at which the tangent is vertical.( Note: If there is more than one write them as a comma separated list, e.g. (1,2),(3,4)) the tangent is vertical.(Note: If there is (64,0) At which t value(s) is the tangent to this curve horizontal? (Note: If there is more than one write them as a comma separated list). Write the point(s) at which the tangent is horizontal. (Note: If there is more than one write them as a comma separated list, e.g. (1,2).(3,4)) (1, -61/(3sqrt(3))), (1, 61/(3sqrt(3))) Use a graphing device to graph the curve and check your work.

Explanation / Answer

1) x =64-t2, y =t3-9t

dx/dt =-2t , dy/dt =3t2-9

vertical tangent => dx/dt =0

-2t =0

t =0

points (x,y)=(64-02,03-9*0)=(64,0)

horizontal tangent => dy/dt =0

=>3t2-9=0

=>t2=3

=>t =-3 ,t =3

at t =-3

x= 64-(-3)2=61, y =(-3)3-9(-3) =63

at t =3

x= 64-(3)2=61, y =(3)3-9(3) =-63

points are (61,63),(61,-63)

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