# High School Calculus Help

• Sep 16th 2008, 11:29 PM
Brownhash
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.

• Sep 16th 2008, 11:36 PM
11rdc11

Take the derivative of the position function

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

\$\displaystyle 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.
• Sep 16th 2008, 11:39 PM
Brownhash
Thanks alot, any help with the others would be much appreciated
• Sep 16th 2008, 11:43 PM
11rdc11
You forgot to post what the equation is in problem 3
• Sep 16th 2008, 11:48 PM
Brownhash
Oh yea sorry hadnt noticed i just copied out the question thats the techers error :D ignore that question please
• Sep 16th 2008, 11:55 PM
11rdc11
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 \$\displaystyle x^3 +2\$ or \$\displaystyle (x-2)^3 -7\$ or etc. Same thing with the parabola. It could be \$\displaystyle x^2\$ or \$\displaystyle (x-5)^2 +6\$ or something else.
• Sep 16th 2008, 11:57 PM
Brownhash
Hmm i think number two is part of number one and never mind number 6. thanks