(4 marks) d) Classify the extreme points of y(x)=2x^3-9x^2+12x e) Find (dy)/(dx) given (i) x^3-3x^2y^3=20(x+y^2) at x=-2,y=1 (4 marks) (ii) y=x^3cos^-1(3x) (3 marks) (iii) y=2^x^(2)ln(4x-14) (4 marks) (3 marks)

d) To classify the extreme points of the function , we need to find the critical points by taking the derivative and setting it equal to zero. Setting , we get: Simplifying, we have: Factoring, we get: So, the critical points are and .To classify these critical points, we can use the second derivative test. Taking the second derivative of , we get: Evaluating at , we get: Since , the critical point is a local minimum.Therefore, the extreme points of the function are a local maximum at and a local minimum at .e) (i) To find for the given equation at , we need to differentiate both sides of the equation with respect to .Differentiating the left side, we get: Simplifying, we have: Rearranging the terms, we get: Factoring out , we have: Solving for , we get: Substituting and into the expression, we get: Therefore, at .(ii) To find for the given function , we need to use the chain rule and the derivative of the inverse trigonometric function.Differentiating with respect to , we get: Simplifying, we have: Therefore, .(iii) To find for the given function , we need to use the chain rule and the derivative of the exponential and logarithmic functions.Differentiating with