Question

If $f(x) = x^{5} - 20x^{3} + 240x$, then $f(x)$ satisfies which of the

Following

• A. It is monotonically decreasing everywhere
• B. It is monotonically decreasing only in $(0,\infty)$
• C. It is monotonically increasing every where
• D. It is monotonically increasing only in $( - \infty,0)$

Answer 1

Answer: (C)

It is monotonically increasing every where

Answer 2

$f^{'}(x) = 5x^{4} - 60x^{2} + 240$

= $5(x^{4} - 12x^{2} + 48) = 5\lbrack(x^{2} - 6)^{2} + 12\rbrack$ ⇒ f^{'}(x) > 0\overset{̶}{\vee}x \in R

i.e., $f(x)$ is monotonically increasing everywhere.