Question

If $f\left(x\right)=x^5-20x^3+240x$, then $f\left(x\right)$ satisfies:

• A. It is monotonically decreasing everywhere
• B. It is monotoniclly decreasing on $(0,\infty )$
• C. It is monotonically increasing on $(-\infty ,0)$
• D. It is monotonically increasing everywhere

Answer 1

Answer: (D)

It is monotonically increasing everywhere

$f\left(x\right)=x^5-20x^3+240x$
$f^{\prime }\left(x\right)=5x^4-60x^2+240$
$f^{\prime }\left(x\right)=5\left[\right(x^2-6{)}^2+12]$
Clearly f'(x)>0 for all $x\in R$
Hence, f(x) is monotonically increasing everywhere.