In this graph, the slope of the tangent line is zero at points where the green curve (the function) has a horizontal tangent line, which corresponds to local maxima, minima, or inflection points with a horizontal tangent. These points indicate where the derivative of the function equals zero.

In your image, the points with a horizontal tangent line, and thus a slope of zero, are at points:

• $G$: Local maximum on the left side.
• $B$: Local minimum near the x-axis.
• $E$: Local maximum on the right side.

These points $G$, $B$, and $E$ represent locations where the slope of the tangent is zero on the curve.

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

Here are 5 additional questions related to the topic:

1. How can we use derivatives to identify points where the slope of the tangent is zero?
2. What is the difference between critical points and inflection points?
3. How can we confirm that a point is a maximum or minimum using the second derivative?
4. How do tangent lines relate to instantaneous rates of change in real-world applications?
5. How does the behavior of the curve change at points where the tangent slope is zero?

Tip: When analyzing curves, look for points where the function changes direction—these often correspond to where the slope is zero.