The diagram shows part of the curve with equation y = 3 + 5x + x 2

Question:

The diagram shows part of the curve with equation y = 3 + 5x + x2 − x3. The curve touches the x-axis at A and crosses the x-axis at C. The points A and B are stationary points on the curve.


a. Show that C has coordinates (3, 0).


b. Using calculus and showing all your working, find the coordinates of A and B.


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