High School Calculus Help

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 (Rofl)

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 (Wink)

i'll help you out with #4

Take the derivative of the position function





B) v(1.5) = ?

C) v(0) = ?

D) v(t) = 24

For the 1st question take the derivative of the function and set it to 0 to find your critical points. Your max and min will occur at your critical points if there are any. Use the 1st or 2nd derivative test to see if it is a max or min.

Thanks alot, any help with the others would be much appreciated

You forgot to post what the equation is in problem 3

Oh yea sorry hadnt noticed i just copied out the question thats the techers error :D ignore that question please

Well what is the equation for problem 2, is it the same for problem 1?

For question 6 its depends what graphs were given.

For instance you could have a cubic like or or etc. Same thing with the parabola. It could be or or something else.

Hmm i think number two is part of number one and never mind number 6. thanks