The curve C has equation y = (x^2 -4x - 2)^2. Point P lies on C and has coordinates (3,N). Find: a) the value of N. b) the equation of the tangent to C at the point P, in the form y=mx+c where m and c are constants to be found. c) determine d^2y/dx^2.

a) Sub x=3 into the given equation. N is found to be 25.b) Finding dy/dx gives me, as the first differential is the gradient.First differentiate the power and then multiply the differential of the expression inside the bracket. general expression for dy/dx = 2(x^2 -4x-2)X(2x-4)dy/dx at point P(3,25) = 2(9 -12 -2)X(6-4) =-20Determine the constant c from the coordinates of point P which is known to lie on the line we are trying to find. 25 = -20(3) + cc = 85Therefore y = 85 - 20xc) Product rule needed to differentiate dy / dx to get the second differential.Product rule - u' v + v' ud^2 y / dx^2 = 4(2x- 4)(x-2) + 4(x^2-4x-2) = 4(2x^2 -8x +8) + 4x^2 - 16x -8 = 12x^2 -48x +24