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Math Help - Need help on some questions regarding applications of differentiation ,rate of change

  1. #1
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    Need help on some questions regarding applications of differentiation ,rate of change

    Hi Guy,

    Am stuck with 3 questions for some questions about application of differentiation.

    Would appreciate if any kind souls can englighten me on how to do the questions thanks !

    NewDocument1(2).pdf
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  2. #2
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    Quote Originally Posted by liukawa View Post
    Hi Guy,

    Am stuck with 3 questions for some questions about application of differentiation.

    Would appreciate if any kind souls can englighten me on how to do the questions thanks !

    NewDocument1(2).pdf

    This is very basic stuff and unless you haven't yet understood anything you must have done some work by yourself. Show it

    and tell where you are stuck.

    Tonio
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  3. #3
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    I might point out that many people will not open "word" files (or many other files). If you cannot take the time to type the problem yourself (and learn LaTex) don't be surprised if some people don't take the time to help you.
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  4. #4
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    Hi Guys.

    Any help please?

    Need help urgently thanks !

    Have posted the questions in JPEG format for easy reading ..


    Need help on some questions regarding applications of differentiation ,rate of change-newdocument1-2-_page_3.jpgNeed help on some questions regarding applications of differentiation ,rate of change-newdocument1-2-_page_1.jpgNeed help on some questions regarding applications of differentiation ,rate of change-newdocument1-2-_page_2.jpg
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  5. #5
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    For 2 of the questions, i have written down the questions here :

    1) The Equation y = [bx2 +1/(1+x)(a-x)] has horizontal asymptote y = -1 and vertical asymptotes x = 1, x=-1. Deduce the value of a and b. Find the turning points of the curve y = [bx2 +1/(1+x)(a-x)] and deduce the nature of the turning point. Sketch the graph indicating clearly the essential geometrical features

    2) An open tank with a square base is to be made from a thin sheet of metal. Find the length of the square base and the height of the tank so that the least amount of paint used to paint the tank with a capacity of 8cm3 ( You may assume that h is the height of the tank and x represents the side of the square base.)

    Please help guys if possible.

    Thanks.
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  6. #6
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    Quote Originally Posted by liukawa View Post
    For 2 of the questions, i have written down the questions here :

    1) The Equation y = [bx2 +1/(1+x)(a-x)] has horizontal asymptote y = -1 and vertical asymptotes x = 1, x=-1. Deduce the value of a and b. Find the turning points of the curve y = [bx2 +1/(1+x)(a-x)] and deduce the nature of the turning point. Sketch the graph indicating clearly the essential geometrical features
    Well, what have you done on this? What is the derivative of y= bx^2+ \frac{1}{(1+x)(a- x)}= bx^2+ (1+x)^{-1}(a- x)^{-1}? What is the definition of "turning point"?

    2) An open tank with a square base is to be made from a thin sheet of metal. Find the length of the square base and the height of the tank so that the least amount of paint used to paint the tank with a capacity of 8cm3 ( You may assume that h is the height of the tank and x represents the side of the square base.)
    What is the formula for the volume of a rectangular solid with square base of side x and height y?

    What is the formula for the surface area?

    Can you solve the equation for volume for y and then replace y in the formula for surface area by that?

    How do you find the minimum value of a function?

    Please help guys if possible.

    Thanks.
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