iran-konkur 2021 Q123

iran-konkur · Other · konkur-riazi_1400_specialized 4 marks Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions
123. Consider the intervals on which $f(x) = \dfrac{x^4}{x^3 - 8}$ is strictly decreasing. What is the minimum total length of these intervals?
(1) $2$ (2) $\sqrt[4]{4}-1$ (3) $2\sqrt[4]{4}$ (4) $2(\sqrt[4]{4}-1)$
\textbf{123.} Consider the intervals on which $f(x) = \dfrac{x^4}{x^3 - 8}$ is strictly decreasing. What is the minimum total length of these intervals?

\medskip
(1) $2$ \hfill (2) $\sqrt[4]{4}-1$ \hfill (3) $2\sqrt[4]{4}$ \hfill (4) $2(\sqrt[4]{4}-1)$

\bigskip