\( 1 \leftarrow \) For the following function, find the intervals on which the function is increasing or decreasing.

To determine where a function is increasing or decreasing, you first need to find its derivative. Once you have the derivative, set it equal to zero to find critical points. Analyze the sign of the derivative in the intervals defined by these critical points. If the derivative is positive, the function is increasing in that interval. If it is negative, the function is decreasing. Remember to check endpoints if you're working within a closed interval! In practice, consider a specific example function like \( f(x) = x^3 - 3x^2 + 4 \). By finding its derivative \( f'(x) = 3x^2 - 6x \) and solving \( f'(x) = 0 \), you can pinpoint critical points at \( x = 0 \) and \( x = 2 \). Test the intervals \( (-\infty, 0) \), \( (0, 2) \), and \( (2, \infty) \) to find the behavior of \( f(x) \). It's a fun exercise that highlights how calculus elegantly maps the landscape of functions!