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The question asks for the gradient of the tangent line to the curve \( y = x^3 - 3x - 10 \) at the point \( (1, -12) \), and then asks to find the equation of the tangent line.

### Steps to solve:

1. **Find the gradient of the tangent line:**
   The gradient of the tangent line can be found using the derivative of the function, since the derivative gives the slope of the tangent at any point.

   Given:
   \[
   y = f(x) = x^3 - 3x - 10
   \]
   The derivative \( f'(x) \) will give us the slope function.

   Differentiate \( f(x) \):
   \[
   f'(x) = 3x^2 - 3
   \]

   Now, substitute \( x = 1 \) to find the gradient at the point \( (1, -12) \):
   \[
   f'(1) = 3(1)^2 - 3 = 3 - 3 = 0
   \]
   So, the gradient of the tangent line at the point \( (1, -12) \) is 0.

2. **Find the equation of the tangent line:**
   The equation of a line can be written as:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.

   Using the point \( (1, -12) \) and the slope \( m = 0 \), we get:
   \[
   y - (-12) = 0(x - 1)
   \]
   Simplifying:
   \[
   y + 12 = 0
   \]
   \[
   y = -12
   \]

Thus, the equation of the tangent line is \( y = -12 \).

Would you like more details on any part of the solution?

### Related Questions:
1. How do you find the tangent line to a curve at a different point?
2. What is the significance of a tangent line with zero slope?
3. How do you determine the derivative of more complex functions?
4. What are other methods to compute the gradient of a tangent line?
5. How would this process change for a different curve equation?

### Tip:
For any cubic or higher-degree polynomial, the derivative will be a lower-degree polynomial, which simplifies finding the slope at any specific point.

Gunakan rumus gradien suatu garis singgung pada kurva y = x^3 - 3x - 10 di titik (1, -12) dan tentukan persamaan garis singgung tersebut?

Learn how to calculate the gradient of the tangent line to the curve y = x^3 - 3x - 10 at the point (1, -12). This problem involves calculus concepts such as derivatives and tangent lines, suitable for students in Grades 10-12.

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