Question

The maximum value of the function $x^3+x^2+x-4$ is

• A. $127$
• B. $4$
• C. Does not have a maximum value
• D. None of the above

Answer 1

The correct option is C

Does not have a maximum value

Explanation for the correct option:

Find the critical points of the given function.

A function $f\left(x\right)=x^3+x^2+x-4$ is given.

Differentiate the given function with respect to $x$.

$f\text{'}\left(x\right)=3x^2+2x+1$

Put $f\text{'}\left(x\right)$ equal to zero to find the critical points.

$$\begin{gathered} 3x^2+2x+1=0 \\ \Rightarrow x=\frac{-2\pm \sqrt{2^2-4\left(3\right)}}{2·3} \\ \Rightarrow x=\frac{-2\pm \sqrt{4-12}}{6} \\ \Rightarrow x=\frac{-2\pm \sqrt{-8}}{6} \\ \Rightarrow x=\frac{-2\pm 2\sqrt{2}i}{6} \end{gathered}$$

Since, $f\left(x\right)$ has no real critical point.

Therefore, the given function $x^3+x^2+x-4$ does not have a maximum value.

Hence, option $C$ is the correct answer.