Can someone please give me a step by step breakdown on how to solve and apparoc these questions

thank you

p.s for question 18 there is no need to finish all 3 parts, just one with the steps explained will help :)

12 a Find the derivative of f(x) = 8x - x2. b Use the factoring f(x) = x(8 - x) to find the x-intercepts of y = f(x), then sketch it. c Find the gradients of the tangents at these two x-intercepts. d Show that the tangent is horizontal at the point where x = 4.18 a Differentiate f(x) = x' - 3x + 2. Hence find the two points on y = x' - 3x + 2 where the tangent is horizontal. b Differentiate f(x) = x* - 18x . Hence find the three points on y = x* - 18x where the tangent is horizontal. c Differentiate f(x) = x* + 6. Hence find the two points on y = x' + 6 where the tangent has gradient 75.19 Sketch the graph of f(x) = x2 - 6x and find the gradient of the tangent at the point A(a, a2 - 60) on the curve. a Hence find the value of a if the tangent has gradient: i o ii 2 iii b Find the value of a if the tangent has angle of inclination 135, c Find the value of a if the tangent is, i parallel to 2x - 3y + 4 = 0, ii perpendicular to 2x - 3y + 4 = 0