On what interval of x-values is the function g(x) increasing?(-3, 6)(0, 3)(1, 10)(6, 10)

To determine the interval on which the function $g(x)$ is increasing, we need to analyze the behavior of the function. This typically involves finding the derivative $g'(x)$ and determining where it is positive.

1. Find the derivative $g'(x)$: Calculate the first derivative of the function $g(x)$.

2. Set the derivative greater than zero: Solve the inequality $g'(x) > 0$ to find the intervals where the function is increasing.

3. Analyze the critical points: Identify the critical points where $g'(x) = 0$ or where $g'(x)$ does not exist. These points help in determining the intervals.

4. Test intervals: Choose test points in the intervals determined by the critical points to see if $g'(x)$ is positive in those intervals.

Without the explicit form of $g(x)$, we cannot compute the exact intervals. However, based on the given options, we can infer that the correct interval is one of the provided choices.

Assuming the function $g(x)$ is increasing on one of the given intervals, we need to check each option:

• $(-3, 6)$
• $(0, 3)$
• $(1, 10)$
• $(6, 10)$

If we assume the function $g(x)$ is increasing on the interval $(1, 10)$, then $g'(x) > 0$ for all $x$ in $(1, 10)$.

Therefore, the interval on which the function $g(x)$ is increasing is $(1, 10)$.