June 2008 C1 Paper Differentiation Question

a) ask student: purpose of differentiation (i), how to perform differentiation (ii) (i) to find the gradient of a curve (ii) multiply the coefficient of x by its indice then minus one from the indici perform this calculation to get dy/dx = 3kx^2 - 2x + 1 b) three steps: 1st: find dy/dx of C at A in terms of k: dy/dx = 3/4k + 2 2nd: find dy/dx of the new equation: dy/dx = 7/2 3rd:  equate the two equations: 3/4k + 2 = 7/2    ->    k = 2 c) now we know k, we can insert k and x-coordinate at A back into original equation to find y value y = -6