Hey guys im stuck on a few questions, if anyone could please give the answers to them I would be very thankfull, I am in a rush as it is for tomorrow

1) For the curve y = x3 – 6x2 + 1 find the values of x at the maximum and minimum points. Verify the nature of the points using the derivative.

2) Find the turning points of the curve and determine their nature.

3) The height, h m, of a ball kicked by Dan Carter in a recent rugby game can be modelled by the equation: , where t is time in seconds. Calculate the maximum height of the ball above the ground.

4) A ball rolls down an inclined plane. The distance S in centimetres that it rolls in t seconds is given by the formula: S = t3 + 3t2 + 3. Find

(a)

(b) its velocity at t = 1.5

(c) its initial velocity

(d) after how many seconds it reaches a velocity of 24 m/s

6) Calculate the minimum vertical distance between the cubic and the parabola , when x is positive.

Thankyou in advance