Question 8 16 Marks Consider The Function F X 2x 8 2x 1 A State The X And Y Intercepts Of The Graph Of Y F X 1 (21.05 KiB) Viewed 49 times
Question 8 16 Marks Consider The Function F X 2x 8 2x 1 A State The X And Y Intercepts Of The Graph Of Y F X 2 (29.62 KiB) Viewed 49 times
Question 8 (16 marks) Consider the function f(x)= 2x-8 (2x-1) (a) State the x-and y-intercepts of the graph of y = f(x). (b) State the equation(s) of any asymptotes to the graph of y=f(x). (c) Show carefully that f'(x)=x+30 (2x-1) (d) Using (c) find the exact coordinates and nature of all stationary points. 10 [2 marks] [2 marks] [3 marks] (4 marks]
(e) Sketch the graph of y=f(x), clearly showing all the information above. [3 marks] (f) Using your graph explain why there are two real solutions to 4x² - 4x + 1 = -2(2x - 8) and no real solutions to 4x² - 4x + 1 = 2(2x-8). (Indicate clearly how your graph has been used.) [2 marks]
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