Final answer:
The equation of the tangent line to the graph f(x) = (x³+4x-1)(x-2) at the point (1, -4) is y = x - 5.
Step-by-step explanation:
To find the equation of the tangent line to the graph, we need to find the derivative of the function at the given point.
The derivative of f(x) = (x³+4x-1)(x-2) is f'(x) = 4x³ - 3x² - 6x + 6.
Substituting x = 1 into the derivative, we get f'(1) = 4(1)³ - 3(1)² - 6(1) + 6 = 1.
So the slope of the tangent line at (1, -4) is 1.
Using the point-slope form of a line, y - y₁ = m(x - x₁), we can write the equation of the tangent line as y - (-4) = 1(x - 1), which simplifies to y = x - 5.