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a tangent to the graph at the point shown has a slope of approximately 0,2,-2 or 1/2

The graph shows a function with a visible inflection point where the tangent line has been drawn horizontally. A horizontal tangent implies that the slope at this point is zero. Therefore, the slope of the tangent at the indicated point is approximately:

**0**

Would you like a deeper explanation on how to analyze slopes of tangents in graphs?

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Here are five follow-up questions that build on this topic:

1. What does it mean for a function to have a horizontal tangent?
2. How can you estimate the slope of a tangent line at different points on a curve?
3. How do inflection points affect the slope of a tangent?
4. How would you find the slope of a tangent line at a point analytically if given the function's equation?
5. How can you use calculus to determine where a function’s tangent slope is zero?

**Tip:** A horizontal tangent line often indicates a local maximum, minimum, or inflection point on a curve.

A tangent to the graph at the point shown has a slope of approximately 0, 2, -2, or 1/2.

Learn how to find the approximate slope of a tangent line at a given point on a function graph. This problem introduces calculus concepts such as derivatives and tangent slopes, suitable for students in Grades 11-12.

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