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, $\frac{dy}{dx} < 0$
$\therefore x\left(3x + 10\right) < 0$
$\Rightarrow \frac{-10}{3} < x < 0$