Question

Let `y=x^3-8x+7a n dx=f(t)dot` If `(dy)/(dt)=2` and `x=3` at `t=0,` then `(dx)/(dt)` at `t=0` is given by 1 (b) `(19)/2` (c) `2/(19)` (d) none of these
A. 1
B. `(19)/(2)`
C. `(2)/(19)`
D. None of these

Answer 1

Correct Answer - 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)`