# Thread: High School Calculus Help

1. ## 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

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.

Take the derivative of the position function

$S = t^3 + 3t^2 + 3$

$v(t) = 3t^2 + 6t$

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.

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

4. You forgot to post what the equation is in problem 3

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

6. 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 $x^3 +2$ or $(x-2)^3 -7$ or etc. Same thing with the parabola. It could be $x^2$ or $(x-5)^2 +6$ or something else.

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