Step 6: Solve for x to find the critical points: x = 1 and x = 2.
Step 7: Determine the intervals to test: (-∞, 1), (1, 2), and (2, ∞).
Step 8: Choose a test point from each interval and plug it into the derivative f'(x) to see if it's positive (increasing) or negative (decreasing).
Step 9: For the interval (-∞, 1), test x = 0: f'(0) = 12 (positive, so increasing).
Step 10: For the interval (1, 2), test x = 1.5: f'(1.5) = -1.5 (negative, so decreasing).
Step 11: For the interval (2, ∞), test x = 3: f'(3) = 12 (positive, so increasing).
Step 12: Combine the results: The function is increasing on the intervals (-∞, 1) and (2, ∞).
Derivative and Critical Points – Understanding how to find the derivative of a function and identify critical points where the function's behavior changes.
Increasing and Decreasing Intervals – Determining where a function is increasing or decreasing based on the sign of its derivative.
Interval Testing – Using test points in intervals defined by critical points to determine the behavior of the function.
