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BITSAT 2018
Exam
BITSAT
Year
2018
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2018 · Mathematics · Application of Derivatives

For which interval the given function f(x) = - 2x^ 3 - 9x^ 2 - 12x...

For which interval the given function f(x)=−2x3−9x2−12x+1f\left(x\right) = - 2x^{3} - 9x^{2} - 12x + 1 is decreasing?

Options

  1. A(−2,∞)\left(- 2, \infty\right)
  2. B(−2,−1)\left(- 2, - 1\right)
  3. C(−∞,−1)\left(- \infty , - 1\right)
  4. D(−∞,−2)\left(- \infty , - 2\right)~or& (−1,∞)\left(- 1, \infty\right)

Correct answer

D. (−∞,−2)\left(- \infty , - 2\right)~or& (−1,∞)\left(- 1, \infty\right)

Step-by-step solution

Given, f(x)=−2x3−9x2−12x+1f′(x)=−6x2−18x−12f\left(x\right) = - 2x^{3} - 9x^{2} - 12x + 1 f^{'}\left(x\right) = - 6x^{2} - 18x - 12To be decreasing f′(x)<0⇒−6x2−18x−12<0⇒x2+3x+2>0⇒(x+2)(x+1)>0f^{'} \left(x\right) < 0 ⇒ - 6x^{2} - 18x - 12 < 0 ⇒ x^{2} + 3x + 2 > 0 ⇒ \left(x + 2\right)\left(x + 1\right) > 0Therefore, either x<−2x < - 2 or x > - 1 x \in \left(-1,\infty\right) or \left(- \infty , -2\right)Hence,Hence, option (d) correct.
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