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Math Help - High School Calculus Help

  1. #1
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    Exclamation 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.

    Thankyou in advance
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  2. #2
    Super Member 11rdc11's Avatar
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    i'll help you out with #4

    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.
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  3. #3
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    Thanks alot, any help with the others would be much appreciated
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  4. #4
    Super Member 11rdc11's Avatar
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    You forgot to post what the equation is in problem 3
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  5. #5
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    Oh yea sorry hadnt noticed i just copied out the question thats the techers error ignore that question please
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  6. #6
    Super Member 11rdc11's Avatar
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    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.
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  7. #7
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    Hmm i think number two is part of number one and never mind number 6. thanks
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