The equation of the crooked line is .
is a point on the crooked line whose abscissa value is , when a small perturbation is introduced on , the position of gets shifted to . In pre-computer era, it is numerically difficult to compute the ordinate of . Therefore the image of on the tangent, , is used to estimate .

- Find the general expression for
, evaluated when . - Write down the equation for the purple line, which is the tangent to the crooked line at
.

- Use the
-slider to explore the effect of the size of perturbation on the the gap between and . - Try the tangent line method to compute the approximate values for
, , , etc.