Edexcel Mathematics Sample paper · Paper 1 · Question 15 · ExamRizz

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Sample paper · Paper 1 · Question 15 · 8 marks

15. y P O x Q Figure 5 Figure 5 shows a sketch of the curve with equation y = f ( x ), where 4 2 sin x f ( x ) = , 0  x  π 2 1 x e− The curve has a maximum turning point at P and a minimum turning point at Q as shown in Figure 5. (a) Show that the x coordinates of point P and point Q are solutions of the equation tan 2 x = 2 (4) (b) Using your answer to part (a), find the x-coordinate of the minimum turning point on the curve with equation (i) y = f ( 2x ). (ii) y = 3 − 2f ( x ).

Lesson: Introduction to Differentiation and First Principles (Polynomials)