3 The diagram shows part of the curve with equation
y = x³ - 6x² + 9x. The curve touches the x-axis at A and
has a local maximum at B.
a Show that the equation of the curve may be written
as y = x(x-3)², and hence write down the
coordinates of A.
b Find the coordinates of B.
c The shaded region R is bounded by the
curve and the x-axis. Find the area of R.
(2 marks)
(2 marks)
(6 marks)
B
R
y=x²-6x²+9x/