Find the maximum and minimum values, if any, of the function
$
g(x) = x^3 + 1
$

Q: Find the maximum and minimum values, if any, of the function $ g(x) = x^3 + 1 $

Explanation: Since $x^3$ is strictly increasing on $\mathbb{R}$, the function $g(x) = x^3 + 1$ is also strictly increasing. \[ \text{Hence, } g(x) \text{ has neither a maximum nor a minimum value on } \mathbb{R}. \]

Question

Find the maximum and minimum values, if any, of the function  
$
g(x) = x^3 + 1
$

Accepted Answer

Explanation: Since $x^3$ is strictly increasing on $\mathbb{R}$, the function $g(x) = x^3 + 1$ is also strictly increasing.

$$
\text{Hence, } g(x) \text{ has neither a maximum nor a minimum value on } \mathbb{R}.
$$

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