Question 4. [20 marks]
(a) There are four points, labeled A to D, on the graph for the function y = x3 + 3x2 + 5x. Find the
coordinates for these points to 2 decimal digits, by using derivatives and algebra. Show your working.
(b) Find the equation of the tangent to the curve at the point where x = 1.
(c) At which other point on the graph, will the tangent be parallel to the tangent at x = 1?
Question 7. [10 marks]
You may use the online plotter on AUTonline for this question.
(a) Sketch neat graphs of the curves y = (x 2)2 and y 3x + 6 = 0 on the same coordinate system.
(b) Find the points of intersection for the two graphs. Show your working and check that the points agree
with the graphs in (a).
(c) Shade the region enclosed by the two curves and use a denite integral to determine the area of this