Question

The interval in which the function $y=x^3+5x^2-1$ is decreasing, is

• A. $\left(0,\frac{10}{3}\right)$
• B. $(0,10)$
• C. $\left(\frac{-10}{3},0\right)$
• D. None of these

Answer 1

Answer: (C)

Given, $y-x^3+5x^2-1$
$\Rightarrow \frac{dy}{dx}=3x^2+10x=x\left(3x+10\right)$
For function to be decreasing, $\frac{dy}{dx}<0$
$\therefore x\left(3x+10\right)<0$
$\Rightarrow \frac{-10}{3}<x<0$