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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The interval in which the function $y=x^3+5 x^2-1$ is decreasing, is
  • A
    $\left(0, \frac{10}{3}\right)$
  • B
    $(0,10)$
  • ✓
    $\left(\frac{-10}{3}, 0\right)$
  • D
    None of these
✓

Answer

Correct option: C.
$\left(\frac{-10}{3}, 0\right)$
(c) : Given, $y=x^3+5 x^2-1$
$
\Rightarrow \frac{d y}{d x}=3 x^2+10 x=x(3 x+10)
$
For function to be decreasing, $\frac{d y}{d x}<0$
x(3x + 10) < 0 => $\frac{-10}{3}$< x < 0 

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