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Let y=x^3-8x+7a n dx=f(t) and (dy)/(dx...

Let `y=x^3-8x+7a n dx=f(t) and (dy)/(dx)=2a n dx=3 at t=0,` then find the value of `(dx)/(dt) at t = 0 `

A

1

B

`(19)/(2)`

C

`(2)/(19)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`y=x^(3)-8x+7 and x=f(t)`
`(dy)/(dx)=2 and x = 3" at "t = 0`
`because" "(dy)/(dx)=(dy//dt)/(dx//dt)`
`rArr" "(dx)/(dx)=(dy//dt)/(dy//dx)`
`rArr" "(dx)/(dt=(2)/(3x^(2)-8)`
`rArr" "because " at "t=0, x=3`
`therefore" "(dx)/(dt)("at "t=0)=(2)/(19)`
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