SPM 2017 Additional Mathematics (Paper 2, Question 2)

The equation of the crooked line is

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

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

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.

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