Q. The function $f(x) = 1 - x^{3} - x^{5}$ is decreasing for
A) $1 \leq x \leq 5$
B) $x \leq 1$
C) $x \geq 1$
D) All values of $x$
Explanation
(d)
Given that, $f(x) = 1 - x^{3} - x^{5}$
On differentiating w.r.t. $x$, we get
$f^{'}(x) = - 3x^{2} - 5x^{4}$
$\Rightarrow \ \ f^{'}(x) = - (3x^{2} + 5x^{4})$
$\Rightarrow \ \ f^{'}(x) < 0$for all values of $x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.