SPM 2019 Additional Mathematics (Paper 2 Question 4)
Given that the equation of the crooked line is and that is located on the axis of symmetry of the crooked line while is the maximum point of the crooked line. The purple line, on the hand, is the tangent to the crooked line at .
Use the purple -slider to change the abscissa of . Write down the -value which minimizes the purple-colored region (the area bounded by the crooked line, its tangent, and its axis of symmetry).
The proper mathematical shorthand to evaluate the area of triangle is
This expression is consistent with the fact that the area of the triangle is minimized incrementally when is moved closer to the axis of symmetry of the crooked line.
Try and see if you can use a non-calculus method to show that the area of the purple region is two-third the size of triangle . [Hint: Archimedes was able to do that without using any calculus back in third century BC]