Find the equations of the tangents to the curve y= x(x-1)(x+2) at the points where the curve cuts the x axis

First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have

Which means that the roots are

Next, we can expand the function definition:

In this form, it is much easier to compute the derivative:

If we evaluate the derivative in the points of interest, we have

This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation

is what we need. The three lines are:

 This is the tangent at x = -2

 This is the tangent at x = 0

 This is the tangent at x = 1

d is the answer

step-by-step explanation: