# How do you find the equation of the tangent line to #f(x) = (x-1)^3# at the point where #x=2#?

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To find the equation of the tangent line to f(x) = (x-1)^3 at the point where x=2, we need to find the slope of the tangent line and the coordinates of the point of tangency.

First, we find the derivative of f(x) using the power rule: f'(x) = 3(x-1)^2.

Next, we substitute x=2 into the derivative to find the slope of the tangent line at x=2: f'(2) = 3(2-1)^2 = 3.

Now, we find the y-coordinate of the point of tangency by substituting x=2 into the original function: f(2) = (2-1)^3 = 1.

Therefore, the point of tangency is (2, 1) and the slope of the tangent line is 3.

Using the point-slope form of a linear equation, we can write the equation of the tangent line as y - 1 = 3(x - 2). Simplifying, we get y = 3x - 5.

Thus, the equation of the tangent line to f(x) = (x-1)^3 at the point where x=2 is y = 3x - 5.

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