QPaperGen

We have,
\[
h(x) = x^3 + x^2 + x + 1 \Rightarrow h'(x) = 3x^2 + 2x + 1
\]
Now, the discriminant of \( h'(x) = 3x^2 + 2x + 1 \) is:
\[
\Delta = (2)^2 - 4(3)(1) = 4 - 12 = -8 < 0
\]
So, the derivative has no real roots.
This implies \( h'(x) \neq 0 \) for all \( x \in \mathbb{R} \).

Also, since the leading coefficient is positive, \( h'(x) > 0 \) for all \( x \in \mathbb{R} \).
Therefore, the function is strictly increasing and has no maximum or minimum.

Hence, \( h(x) = x^3 + x^2 + x + 1 \) does not have any local maxima or minima.