Question 4 -2 supertrain F E A part of the track for Tim's model train follows the curve passing through A, B, C, D, E and F shown above. Tim has designed it by putting axes on the drawing as shown. The track is made up of two curves, one to the left of the y-axis and the other to the right. B is the point (0,7). The curve from B to F is part of the graph of f(x) = px + qx+x+s where p, q, r and s are constants and f'(0)=4.25. a. i. Show that s=7. ii. Show that r 4.25. The furthest point reached by the track in the positive y direction occurs when x = 1. Assume p > 0. b. i. Use this information to find q in terms of p. ii. Find f(1) in terms of p. iii. Find the value of a in terms of p for which f'(a)=0 where a > 1. 17 iv. If a=- . show that p=0.25 and q=-2.5. For the following assume f(x) = 0.25x-2.5x+4.25x+7. c. Find the exact coordinates of D and F. 2+1+1+2 6 marks 2 marks d. Find the greatest distance that the track is from the x-axis, when it is below the x-axis, correct to two decimal places. 1 mark a The curve from A to B is part of the graph with equation g(x)= where a and b are positive real constants. 1-bx The track passes smoothly from one section of the track to the other at B (that is, the gradients of the curves are equal at B). e. Find the exact values of a and b. f. 3 marks Find the area of the shaded section bounded by the track between x=-2 and D, correct to two decimal places.