Algebra

Determine the interval(s) on which the function is (strictly) increasing.

Step-by-step solution with explanation

Final Answer

No function was provided. Please resubmit the problem with the full function expression so all increasing intervals can be found.

Step-by-step solution

1

Identify the function to analyze

No function was included in the problem. To find increasing intervals, we need an explicit function such as f(x) = x² or f(x) = x³ - 3x. Please resubmit with the full function.
2

Find the derivative of the function

We would differentiate f(x) to get f'(x). The derivative tells us the slope of the function at every point.
3

Set derivative greater than zero

A function is strictly increasing wherever its derivative is positive. We solve this inequality to find those x-values.

Understanding this problem

Learning Insight

A function increases when its slope is positive. The derivative f'(x) measures slope, so solving f'(x) > 0 directly reveals every interval where the output grows as x moves right. This connects the geometric idea of 'going uphill' to algebra.

Quick Tip

Find where f'(x) = 0 first (critical points), then test one x-value in each resulting interval in f'(x). Positive result → increasing; negative result → decreasing.

Common Mistake

Students often include the critical points (endpoints of intervals) and write closed brackets like [a, b] instead of open brackets (a, b). Strictly increasing means f'(x) > 0, not ≥ 0, so critical points where f'(x) = 0 are excluded.