The slope of the tangent line to the curve  at the point  is:

slope = 

To find the slope of the tangent line to a curve at a specific point, we generally need to:

1. Differentiate the curve's equation with respect to \( x \) to get \( \frac{dy}{dx} \), which represents the slope of the tangent at any point on the curve.
2. Substitute the \( x \)-coordinate of the given point into the derivative to find the slope at that specific point.

Could you provide the equation of the curve and the point of tangency so that we can proceed with these steps?

If you need further clarification, please let me know.

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1. What is the process for finding the derivative of a function?
2. How do we interpret the derivative geometrically?
3. Why is the tangent line’s slope important in calculus?
4. What does a zero slope indicate about a tangent line at a point?
5. How can we find the equation of the tangent line itself, not just the slope?

**Tip:** The derivative of a function at a point gives us the instantaneous rate of change at that specific point.

The slope of the tangent line to the curve at the point is: slope =

Learn how to find the slope of the tangent line to a curve at a specific point by differentiating the curve's equation. This solution covers fundamental calculus concepts like derivatives and tangent lines, ideal for students in Grades 11-12.

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