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Use the graph of the function f Given in the graph. List the values of X at which F has a local maximum

From the graph of the function \( f(x) \), let's identify the points where the function has local maximums. A local maximum occurs at points where the function reaches a peak value that is higher than the values immediately surrounding it.

**Identifying Local Maximums:**

Looking at the graph:

1. The first local maximum occurs near \( x = -7 \).
2. The second local maximum occurs near \( x = 2 \).

These are the approximate x-values where the function \( f(x) \) has local maximum points.

Would you like more details on how to identify these points, or do you have any other questions?

**Follow-up Questions:**

1. How can you determine local minima from a graph?
2. What is the significance of the points where the derivative of a function is zero?
3. How do you find inflection points on a graph?
4. What are global maximums, and how do they differ from local maximums?
5. How can we estimate the values of \( f(x) \) at these local maximum points?

**Tip:** To find local maximums or minimums, look for points where the slope of the function changes from positive to negative (for maximums) or from negative to positive (for minimums).

Use the graph of the function f given in the graph. List the values of X at which F has a local maximum.

Identify the values of x at which a function f(x) has local maximums using the graph. Understand critical points, the first derivative test, and the second derivative test. Suitable for high school students studying calculus.

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