Question

The function $f(x)=1-x^3-x^5$ is decreasing for

• A. $1\le x\le 5$
• B. $x\le 1$
• C. $x\ge 1$
• D. all values of $x$

Answer 1

Answer: (D)

Given that, $f(x)=1-x^3-x^5$
On differentiating w.r.t. $x$, we get
$f(x)=-3x^2-5x^4$
$\Rightarrow f\left(x\right)=-\left(3x^2+5x^4\right)$
$\Rightarrow f\left(x\right)<0$ for all values of $x$.