Question: 9. [Maximum mark: 16] Let f(x) = In 5x - where x > 0, KER*. kx (a) Show that f'(x) = 1 - In 5x

9. [Maximum mark: 16] Let f(x) = In 5x - where x > 0, KER*. kx (a) Show that f'(x) = 1 - In 5x [3] The graph of f has exactly one maximum point P. (b) Find the x-coordinate of P. [3] The second derivative of f is given by f*(x) = 212x - 2 . The graph of f has exactly one kx' point of inflexion Q. (c) Show that the x-coordinate of Q is- [3] The region R is enclosed by the graph of f, the x-axis, and the vertical lines through the maximum point P and the point of inflexion Q. P Q R (d) Given that the area of R is 3, find the value of k. [7]

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