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The function f, of, xf(x) is graphed below. How many points on the graph represent a relative maximum?

To determine how many points on the graph represent a **relative maximum**, we need to examine where the graph has peaks. A **relative maximum** occurs when a function changes from increasing to decreasing, forming a peak.

Looking at the graph, we can identify:

- The graph rises, reaches a peak at point **a**, and then starts decreasing. This is a relative maximum.
- The graph reaches another peak at point **c**, where it switches from increasing to decreasing again. This is also a relative maximum.

Thus, there are **two points** on the graph that represent relative maxima: points **a** and **c**.

Would you like further details, or have any other questions?

Here are 5 related questions to consider:
1. What is the definition of a relative minimum on a graph?
2. How can you determine whether a point is a relative maximum by using the derivative of a function?
3. What is the difference between a relative maximum and an absolute maximum?
4. How would you calculate the exact coordinates of the relative maxima if the function were given?
5. How do inflection points affect the graph of a function?

**Tip**: To confirm a relative maximum or minimum, you can use the first and second derivative tests in calculus!

The function f(x) is graphed below. How many points on the graph represent a relative maximum?

Learn how to identify the relative maxima from a graph of the function f(x). This problem covers key calculus concepts such as relative maxima, first derivative tests, and graph analysis, suitable for Grades 11-12.

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