The graph you described shows a function $f(x)$ that has a periodic-like behavior with alternating rises and falls.

Identifying Local Minima:

A local minimum occurs where the function changes from decreasing to increasing. From the description of the graph, we can identify the following key points:

• The function falls from $(-9, 9)$ to $(-3, -9)$, meaning at $x = -3$, the function reaches a low point (local minimum).
• The function falls again from $(3, 9)$ to $(9, -9)$, so at $x = 9$, the function also reaches another low point (local minimum).

Thus, the local minima occur at $x = -3$ and $x = 9$.

Answer:

The values of $x$ at which $f(x)$ has local minima are:

$x = -3, 9$

Would you like a more detailed explanation of how to find local minima or have further questions?

Related Questions:

1. What are the values of $x$ at which $f(x)$ has local maxima?
2. What is the behavior of the function as $x \to -\infty$ and $x \to \infty$?
3. Can you identify points of inflection on this graph?
4. How do we distinguish between a local minimum and a global minimum?
5. How can you use the first and second derivative tests to find minima?

Tip:

When identifying local extrema, always check where the function changes direction (increasing to decreasing for maxima, decreasing to increasing for minima).