further differentiations

Question 5 The figure below shows the curve y = 3 In x + x - x2 The curve crosses the x-axis at P and Q, and has a turning point at R. the x- coordinate of Q is approximately 2.05. Verify that the coordinates of P are (1, 0) [1] Find the coordinates of R, giving the y-coordinate correct to 3 significant figures. Find day 2x2, and use this to verify that R is a maximum point [9] Question 6 The figure below shows part of the curve y = e 5* sin x for all x - It 2n Show that the x coordinate of the turning point P satisfies the equation tan x = 5 Hence find the coordinates of P [6]