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Let y=x^(3)-8x+7 and x=f(t)." If "(dy)/(...

Let `y=x^(3)-8x+7 and x=f(t)." If "(dy)/(dt)=2 and x=3 at t = 0," `then
` "(dx)/(dt)` at t = 0 is given by`

Text Solution

Verified by Experts

`"Let "y=x^(3)-8x+7`
`therefore" "(dy)/(dx)=3x^(2)-8`
It is given that when t=0, x=3. Therefore, when t=0,
`(dy)/(dx)=3xx3^(2)-8=19`
`"Also ", (dy)/(dx)=(dy//dt)/(dx//dt)`
Since when `t=0, (dy)/(dx)=19 and (dy)/(dt) = 2, from (1)`
`19=(2)/(dx//dt) or (dx)/(dt)=(2)/(19)`
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