Chapter 4 - Applications of the Derivative - 4.3 The Mean Value Theorem and Monotonicity - Exercises - Page 189: 36

$f(x) $ has no critical points and $ f(x)$ is increasing for all $x$.

Given $$y=x^{5}+x^{3}+x$$ Since $$f'(x) = 5x^4+3x^2+1 $$ Then for all $x$, we have $f'(x)\geq 1$. Hence, $f(x) $ has no critical points and $ f(x)$ is increasing for all $x$.