Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
The equation of the curve is;
y = -½(x+2)²(x-4)
y = -½(x²+4x+4)(x-4)
y = -½(x³-12x-16)
y = -½(x³)+6x+8
It implies;
dy/dx = -½(3x²)+6
For dy/dx = 0
x = 2
Therefore;
y = -½(2³)+6*2+8
y = 16
At the maximum turning point P.
P(2, 16)
Shaded area is;
Area under the curve at point (0, 0) and (4, 0) - Area triangle with height (64/√(65)) units and base (8/√(65)) units.
= 48 - ½((64/√(65))(8/√(65)))
= 48 - ½(64*8)/65
= 48 - (256/65)
= 2864/65 square units.
