can anyone help with calculus? please?

Discussion in 'The Lounge' started by julie124, Mar 19, 2006.

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  1. julie124

    julie124 Private E-2

    there are a couple of problems that are going to be on my final, I was woundering if anyone could help me with these examples..
    1.A boy flying a kite holds a string 5 feet above the ground level. The string is payed out at the rate of 2 feet/second as the kite moves horizontally at an altitude of 105 feet. Assuming there is no sag in the string, find the rate at which the kite is moving (horizontally) when 125 feet of string has been payed out.and draw a graph

    2. Goven F (x)= 3x to the power of 4 - 4X to the power of 3, find A)the x and Y intercpts, B) The points of max/min and C) the inflection points. Use approiate testsand draw a graph.

    3. Using implicit differentiation, find y' given: X to the power of 3 + y to the power of 3=1. Now prove that y"=2x/y to the power of 5

    if anyone can help me I would love it.. been trying for a week ont hese questions thnaks anyways
     
  2. laurieB

    laurieB MajorGeek

    ha, ha, ha, ha,
     

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  3. julie124

    julie124 Private E-2

    whats so funny? i asked a question in hope to get it answered at least some help..
     
  4. laurieB

    laurieB MajorGeek

    so sorry. didn't mean to be rude, which of course it was. i was just in the middle of getting my son to do his maths homework. apologies, apologies.
     
  5. julie124

    julie124 Private E-2

    do you know how to do it?
     
  6. Maxwell

    Maxwell Folgers

    These are easy problems but the margin in this post is too small to put the solution. :D (Fermat's last theorem, q.v.).

    Anyway, as a Mathematics graduate I will give you some hints rather than the complete solution so that you can learn and work out the rest and at least you get some credit.

    1) I think your question wordings could be improved since you could say ignoring mass, atmospherical and gravity conditions the kite will still pay out at 2 feet/sec at any altitude. I have a feeling that there is something missing in the question.

    2) Are you sure you mean F(x) = 3x^4 - 4x^3 ? If so, where does y come into this equation? Is F(x)=y?

    For A) you substitute for x=0 and then y=0 and solve the corresponding equations for the intercepts on the axes. For B) and C) you differentiate the equation and solve for when the differrential is zero to find min/max/inflection, i.e., solve F'(x)=0. To distinguish the solutions for F'(x) = 0, you evalulate F''(x) at the solution points and the value is positive, negative or zero correspond to the type of solution, i.e., turning point.

    3) Your equation is x^3 + y^3 = 1. For y' differentiate each term with respect to x and rearrange the equation (hint use rule 6 below). Similarly for y''.



    Rules of differentiation:

    d ( 1 ) / dx = 0
    d ( x ) / dx = 1
    d ( x^2 ) / dx = 2x
    d ( x^n ) / dx = n x^(n-1)
    d ( aF(x) ) / dx = a d ( F(x) ) / dx
    d ( F(x) + G(x) ) / dx = d ( F(x) ) / dx + d ( G(x) ) / dx
    and there are rules for d ( F(x)G(x) ) / dx and d ( F(G(x)) ) / dx, the latter being the differentiation of a function of a function. You really need several lectures and text books to do the subject any justice.

    note that:

    F'(x) = d ( F(x) ) / dx
     
  7. julie124

    julie124 Private E-2

    thank you.. yeah thats what the question says.. i thought it was weird too, because well I kinda understands it but,these equations are really weird....
    I don't have any examples at all in my text or in my notes.. its weird thanks you anyways..
     
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