# How do you find the equation of the tangent line to a derivative of a function #3x^2-12# at f'(1)?

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To find the equation of the tangent line to the derivative of a function at a specific point, you can follow these steps:

- Find the derivative of the original function.
- Evaluate the derivative at the given point to find the slope of the tangent line.
- Use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, to write the equation of the tangent line.

In this case, the original function is f(x) = 3x^2 - 12.

- Find the derivative of f(x) using the power rule: f'(x) = 6x.
- Evaluate the derivative at x = 1: f'(1) = 6(1) = 6. This gives us the slope of the tangent line.
- Use the point-slope form with the given point (1, f'(1)) = (1, 6): y - 6 = 6(x - 1).

Therefore, the equation of the tangent line to the derivative of the function 3x^2 - 12 at f'(1) is y - 6 = 6(x - 1).

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