2022 BTYSS P2 Q9

2022 BTYSS P2 Q9

Secondary 4
9 marks

The diagram shows the line \(y=x+3\) intersecting the curve \(y=-x^3+2x^2+5\) at the point \(A(2,5)\).

  1. Show that the curve \(y=-x^3+2x^2+5\) intersects the line \(y=x+3\) at only one point, \(A(2,5)\).[4]
  2. Find the area of the shaded region.[5]

Solution:

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Answer:(a) Only real intersection \(A(2,5)\). (b) \(\dfrac{10}3\text{ units}^2\).

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