Figure 3 Figure 3 shows a sketch of part of the curve with equation y = 7x^2(5 - 2?x), x ? 0 The curve has a turning point at the point A, where x > 0, as shown in Figure 3. a) Using calculus, find the coordinates of the point A. The curve crosses the x-axis at the point B, as shown in Figure 3. b) Use algebra to find the x coordinate of the point B. The finite region R, shown shaded in Figure 3, is bounded by the curve, the line through A parallel to the x-axis and the line through B parallel to the y-axis. c) Use integration to find the area of the region R, giving your answer to 2 decimal places.
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