8 4. The curve with equation y = f (x) where f (x) = x2 + ln (2x2 − 4x + 5) has a single turning point at x = α (a) Show that α is a solution of the equation 2x3 − 4x2 + 7x − 2 = 0 (4) The iterative formula xn + 1 = 1 7 (2 + 4xn 2 − 2xn 3) is used to find an approximate value for α. Starting with x1 = 0.3 (b) calculate, giving each answer to 4 decimal places, (i) the value of x2 (ii) the value of x4 (3) Using a suitable interval and a suitable function that should be stated, (c) show that α is 0.341 to 3 decimal places. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
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Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
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