Question

the function f(x) is graphed below how many points on the graph represent the relative extreme value

Answer 1

To determine how many points on the graph of the function \( f(x) \) represent relative extreme values (relative maxima or minima), you typically look for the following:

1. **Critical Points**: These are points where the derivative of the function is zero (i.e., \( f'(x) = 0 \)) or undefined. At these points, the function potentially has relative extrema.

2. **Behavior of the Derivative**: To classify these critical points, you can analyze how the derivative changes sign before and after each critical point:
- If \( f'(x) \) changes from positive to negative at a point, that point is a relative maximum.
- If \( f'(x) \) changes from negative to positive, that point is a relative minimum.

3. **Endpoints**: If you are considering the entire graph, endpoints could also represent extreme values, though they are not "relative" in the same sense as those determined by critical points.

If you're looking directly at the graph and trying to identify these points visually, you should focus on the peaks and valleys in the graph. Each peak (where the direction of the graph switches from going up to going down) is a relative maximum, and each valley (where the direction of the graph switches from going down to going up) is a relative minimum.

For an exact count of how many points represent relative extreme values, please refer to the specific graph you are analyzing. Count the number of distinct peaks and valleys, and that will give you the total number of relative extreme values.