QUESTION 10 The graph defined by f(x) = x + ax + bx + c is...

  

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QUESTION 10 The graph defined by f(x) = x + ax + bx + c is shown along with its tangent g(x) = mx + c. Both graphs cut the y-axis at D. The graph of cuts the x-axis at (-3; 0), (2; 0) and (5;0). A B 10.1 Show that a -4, b = -11 and c = 30. (4) 10.2 Determine the coordinates of A, the turning point of f. (4) 10.3 Determine the equation of g. (2) 10.4 Determine the values of x for which: 10.4.1 f'(x) <0 (2) 10.4.2 f"(x) > 0 (3) 10.5 For which values of k will f(x) = g(x) + k have non-real roots? (1) [16] QUESTION 10 The graph defined by f(x) = x + ax + bx + c is shown along with its tangent g(x) = mx + c. Both graphs cut the y-axis at D. The graph of cuts the x-axis at (-3; 0), (2; 0) and (5;0). A B 10.1 Show that a -4, b = -11 and c = 30. (4) 10.2 Determine the coordinates of A, the turning point of f. (4) 10.3 Determine the equation of g. (2) 10.4 Determine the values of x for which: 10.4.1 f'(x) <0 (2) 10.4.2 f"(x) > 0 (3) 10.5 For which values of k will f(x) = g(x) + k have non-real roots? (1) [16]