a tangent to the graph of the function at the point shown has a slope of

To find the slope of the tangent line to a graph at a given point, you need to determine the derivative of the function at that point. The derivative of a function \( f(x) \) at a point \( x = a \), denoted as \( f'(a) \), represents the slope of the tangent line at that point.

Here are the steps typically involved:

1. **Find the derivative**: If the function is given as \( f(x) \), compute the derivative \( f'(x) \) using differentiation rules.
2. **Evaluate the derivative at the point**: After finding \( f'(x) \), substitute the \( x \)-coordinate of the point into the derivative to get the slope of the tangent line.

If you have the equation for the function or the point’s coordinates, I can walk you through these steps in detail. You can upload the function or the graph, and I'll help find the slope of the tangent line at the given point.

Would you like to upload the graph or provide the function details? 

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Here are some related questions you might find helpful:

1. What is the derivative of a given polynomial function?
2. How do you compute the slope of a tangent line using implicit differentiation?
3. How do you differentiate trigonometric functions like \( \sin(x) \) and \( \cos(x) \)?
4. What’s the geometric interpretation of the slope of a tangent line?
5. How do you find the equation of a tangent line once you know its slope?

**Tip**: The slope of a tangent line is essentially the instantaneous rate of change of the function at a specific point.

Learn how to find the slope of a tangent line to a graph at a specific point using derivatives. This step-by-step guide covers key calculus concepts such as differentiating functions and evaluating the derivative at a point. Suitable for students in Grades 11-12.

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