Question

The interval in which the function $f\left(x\right)=x^3$ increases less rapidly than $g\left(x\right)=6x^2+15x+5$ is :

• A. $(-\infty ,-1)$
• B. $(-5,1)$
• C. $(-1,5)$
• D. $(5,\infty )$

Answer 1

The correct option is C $(-1,5)$

$\text{Increasing}\text{rate =}\frac{d}{dx}\left(f_1{x}_1\right)$

$\text{f}\left(x\right)=6x^2+15x+5$

$\text{f}\left(x\right)=12x+15$

$\frac{d}{dx}{\left(x\right)}^3<\frac{d}{dx}\left(6x^2+15x+5\right)$

$\text{3}{\text{x}}^2\text{< 12x + 15}$

$\text{3}{\text{x}}^2-12x-15<0$

$x^2-4x-5<0$

$x^2-5x+x-5<0$

$\left(x+1\right)\left(x-5\right)<0$

$x\in \left(-1,5\right)$