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A curve parametrically given by x=t+t^(3...

A curve parametrically given by `x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "` `(dy)/(dx)=(1)/(2)`?

A

`1//3`

B

2

C

3

D

1

Text Solution

Verified by Experts

`(dy)/(dx)=(dy//dt)/(dx//dt)=(2t)/(1+3t^(2))=(1)/(2)`(given)
`rArr" "3t^(2)-4t+1=0`
`rArr" "(3t-1)(t-1)=0`
`rArr" "t=(t)/(3),t=t`
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