Question

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

• A. monotonic increasing everywhere
• B. monotonic decreasing only in $(0,\infty )$
• C. monotonic decreasing everywhere
• D. monotonic increasing only in $(-\infty ,0)$

Answer 1

The correct option is A monotonic increasing everywhere

f(n)=$x^5-20x^3+240x$ $f\left(n\right)=5x^4-60x^2+240$ $f^{\prime }\left(n\right)=5x^4-60x^2+240$

$5x^2-60x^2+240=0$

$5x^4-60x^2+240=0$

$x^2-12x^2+48=0$

D<0

So, f(n) is always increasing