Answer
True
Work Step by Step
A critical number is a value of $x$ for which the function is undefined or its first derivative is zero.
$g(x) = f(x) + k$, where $k$ is a constant, will have the same critical numbers as $f(x)$ has the same domain and the same first derivative.
Example: $f(x)=x^{4} + 8x^{3} + 18x^{2}$
Critical Numbers: $x = 0, -3$
$g(x)=x^{4} + 8x^{3} + 18x^{2} +5$
Critical Numbers: $x = 0, -3$
