Question

For which interval, the given function $f(x)=-2x^3-9x^2-12x+1$ is decreasing?

• A. $(-2,\infty )$
• B. $(-2,-1)$
• C. $(-\infty ,-1)$
• D. $(-\infty ,-2)$ and $(-1,\infty )$

Answer 1

Answer: (D)

Given, $f(x)=2x^3-9x^2-12x+1$ $\Rightarrow$ $f^{\prime }(x)=-6x^2-18x-12$ To be decreasing, $f^{\prime }(x)<0$ $\Rightarrow$ $-6x^2-18x-12<0$ $\Rightarrow$ $x^2+3x+2>0$ $\Rightarrow$ $(x+2)(x+1)>0$ $\therefore$ Either $x<-2$ or $x>-1$ $\Rightarrow$ $x\in (-1,\infty )$ or $(-\infty ,-2)$