For what values of x  is the rate of increase of `x^3-5x^2+5x+8`  is twice the rate of increase of x ?

Options

A. `-3, -(1)/(3)`
B. `-3, (1)/(3)`
C. `3, -(1)/(3)`
D. `3, (1)/(3)`

Answer

D

Explanation

Let `y=x^(3)-5x^(2)+5x+8`. Then,
`(dy)/(dt)=(3x^(2)-10x+5)(dx)/(dt)`
When `(dy)/(dt)=2(dx)/(dt)`, we have
`(3x^(2)-10x+5)(dx)/(dt)=2(dx)/(dt)`
`implies 3x^(2)-10x+3=0`
`implies(3x-1)(x-3)=0`
`impliesx=3,(1)/(3)`