Final answer:
To determine where a function is increasing, we look at its first derivative. If the first derivative is positive across an interval, then the function is increasing on that interval.
Step-by-step explanation:
When finding where a function is increasing, consider the first derivative of the function. The first derivative of a function gives us the rate of change of the function's value with respect to changes in its input. If the first derivative is positive over a certain interval, the function is increasing on that interval. Conversely, if the first derivative is negative on an interval, the function is decreasing there.
For example, if we have the function f(x) = x^2, its first derivative, f'(x) = 2x, tells us that f(x) is increasing when x > 0 and decreasing when x < 0. The second derivative, while not the correct choice for this question, would tell us information about the concavity of the function and not directly about whether the function is increasing or decreasing.
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