June 2022 · Paper 2 · Question 6 · 7 marks☆ SaveShow the mark schemeNext questionLesson: Introduction to Differentiation and First Principles (Polynomials)
![6. y x Oα P Figure 2 Figure 2 shows a sketch of part of the curve with equation y = f(x) where f(x) = 8 sin 1 2x − 3x + 9 x > 0 and x is measured in radians. The point P , shown in Figure 2, is a local maximum point on the curve. Using cal culus and the sketch in Figure 2, (a) find the x coordinate of P, giving your answer to 3 significant figures. (4) The curve crosses the x -axis at x = α , as shown in Figure 2. Given that, to 3 decimal places, f(4) = 4.274 and f(5) = −1.212 (b) explain why α must lie in the interval [4, 5] (1) (c) Taking x0 = 5 as a first approximation to α, apply the Newton-Raphson method once to f(x) to obtain a second approximation to α. Show your method and give your answer to 3 significant figures. (2) 13 14 15](https://firebasestorage.googleapis.com/v0/b/plewcsat1.firebasestorage.app/o/examboard%2Fedexcel%2Fsubject%2Fmathematics%2Fa_level%2Fpure_mathematics%2Fpaper_2%2F2022%2Fjune%2Fquestions%2FQ6.png?alt=media)
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