Question

The function $x^4–4x$ is decreasing in the interval

• A. $[–1,1]$
• B. $(–\infty ,1)$
• C. $[1,+\infty )$
• D. None of these

Answer 1

The correct option is B

$(–\infty ,1)$

The explanation for the correct answer:

Solve for the interval in which the function $x^4–4x$ is decreasing.

$f\left(x\right)=x^4–4x$

The function$f\left(x\right)$ is said to be decreasing, if $f\text{'}\left(x\right)<0$

$\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$

Now putting $f\text{'}\left(x\right)<0$

$$\begin{gathered} 4(x^3–1)<0 \\ (x^3–1)<0 \\ {x}^3<1 \\ x<1 \\ x\in (–\infty ,1) \end{gathered}$$

$\therefore f\left(x\right)$is decreasing on $(–\infty ,1).$

Hence, option(B) is the correct answer.