Mark the correct alternative in the following:

For what values of x is the rate of increase of x³ – 5x² + 5x + 8 is twice the rate of increase of x?

Let P(x)=x³-5x²+5x+8 – (1)

Given that , We have to calculate x

Differentiating (1) with respect to t, we get

3x²-10x+5=2

⇒ 3x²-10x+3=0

Factorizing the above quadratic equation, we get

(3x-1)(x-3)=0

⇒ or x=3