Final answer:
Intervals where f(x) is positive can be found using Algebra to test intervals between roots, Calculus through Integration to find areas under the curve, and Differentiation to apply the first derivative test, or by visually inspecting a graph produced by a calculator.
Step-by-step explanation:
To find all intervals where f(x) is positive, we can use several approaches from mathematics, such as:
- Algebra: By finding the roots of the function and testing the intervals between the roots to determine where the function is positive.
- Calculus: Using Integration to determine the areas under the curve, which can help identify where the function is above the x-axis.
- Differentiation: Applying the first derivative test to find where the function is increasing, which helps in identifying regions where f(x) is likely to be positive.
Furthermore, advanced calculators like the TI-83, 83+, or 84 can be used to graph the function and visually determine the intervals where f(x) is above the x-axis.