Question

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

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

Answer 1

The correct option is D $(\infty ,-2)$ or $(-1,\infty )$

$f\left(x\right)=-2x^3-9x^2-12x+1$

$f^{\prime }\left(x\right)=-6x^2-18x-12$

$\because f^{\prime }\left(x\right)$ is decreasing, so,

$f^{\prime }\left(x\right)<0$

$-6x^2-18x-12<0$

$6x^2+18x+12>0$

$6(x+2)(x+1)>0$

option 'd' is correct.