Question

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

• A. $-3,-\frac{1}{3}$
• B. $-3,\frac{1}{3}$
• C. $3,-\frac{1}{3}$
• D. $3,\frac{1}{3}$

Answer 1

The correct option is D $3,\frac{1}{3}$

Let $y=x^3-5x^2+5x+8$. Then,
$\frac{dy}{dx}=(3x^2-10x+5)\frac{dx}{dt}\text{When}\frac{dy}{dt}=2\frac{dx}{dt},\text{we have}(3x^2-10x+5)\frac{dx}{dt}=2\frac{dx}{dt}\Rightarrow 3x^2-10x+3=0\Rightarrow (3x-1)(x-3)=0\Rightarrow x=3,\frac{1}{3}$.
Hence (d) is the correct answer.