(c) Find f′(x). (3) (d) Find f′(2). (2) (e) Write down the coordinates of the local maximum point on the graph of f. (2) (f) Find the range of f. (3) (g) Find the gradient of the tangent to the graph of at = 1. f x (2) There is a second point on the graph of at which the tangent is parallel to the tangent at = 1. f x (h) Find the of this point. x-coordinate (2) (Total 20 marks) 11. The function is defined by = 1.5x + 4 + , 0. f(x) f(x) x ≠ (a) Write down the equation of the vertical asymptote. (2) (b) Find f′(x). (3) (c) Find the gradient of the graph of the function at = x –1. (2) (d) Using your answer to part (c), decide whether the function is increasing or decreasing f(x) at = Justify your answer. x –1. (2) (e) Sketch the graph of for 10 and 20. f(x) x y –10 ≤ ≤ –20 ≤ ≤ (4) P1 is the local maximum point and P2 is the local minimum point on the graph of f(x). (f) Using your graphic display calculator, write down the coordinates of P1 and P2. (4) (g) Using your sketch from (e), determine the range of the function for 10. f(x) x –10 ≤ ≤ (3) (Total 20 marks) 12. Consider the function = 3x2 24x + 30. f(x) x3 – – (a) Write down f(0). (1) (b) Find f′(x). (3)
(c) Find f′(x). (3) (d) Find f′(2). (2) (e) Write down the coordinates of the local maximum point on the graph of f. (2) (f) Find the range of f. (3) (g) Find the gradient of the tangent to the graph of f at x = 1. (2) There is a second point on the graph of f at which the tangent is parallel to the tangent at x = 1. (h) Find the x-coordinate of this point. (2) (Total 20 marks) 11. The function f(x) is defined by f(x) = 1.5x + 4 + , x ≠ 0. (a) Write down the equation of the vertical asymptote. (2) (b) Find f′(x). (3) (c) Find the gradient of the graph of the function at x = –1. (2) (d) Using your answer to part (c), decide whether the function f(x) is increasing or decreasing at x = –1. Justify your answer. (2) (e) Sketch the graph of f(x) for –10 ≤ x ≤ 10 and –20 ≤ y ≤ 20. (4) P1 is the local maximum point and P2 is the local minimum point on the graph of f(x). (f) Using your graphic display calculator, write down the coordinates of P1 and P2. (4) (g) Using your sketch from (e), determine the range of the function f(x) for –10 ≤ x ≤ 10. (3) (Total 20 marks) 12. Consider the function f(x) = x3 – 3x2 – 24x + 30. (a) Write down f(0). (1) (b) Find f′(x). (3)
MOCK-EXAM-REVIEW-Topic-6-Mar-2014.docx