1. The problem is to investigate the sign of the derivative of a function, which helps us understand where the function is increasing or decreasing. 2. The derivative of a function $f(x)$, denoted $f'(x)$, gives the rate of change of the function at any point $x$. 3. To investigate the sign of $f'(x)$, we find the critical points by solving $f'(x) = 0$. 4. Then, we test intervals between critical points to determine if $f'(x)$ is positive (function increasing) or negative (function decreasing) in those intervals. 5. This process helps us identify local maxima, minima, and intervals of increase or decrease. 6. Without a specific function, this is the general method to investigate the sign of the derivative.