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Math Help - S.o.s.

  1. #1
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    Lightbulb S.o.s.

    Hi everyone!

    I need some help with few problems. I would really appreciate if someone could help me!


    Here is the problems :

    1.



    The relation between the price (p) per unit of a product and the number of units sold (x) is given by:

    p=50-0.025

    x


    a) Write down the expression for the total income function ()Ix
    b) Write down the expression for the marginal income function.
    c) For which value of x is the income at its maximum and what is the price in this situation?
    d) Express the demand x(p) as a function of the price p.
    e) Find an expression of the elasticity of the demand with respect to p.
    f) For which value of p is the elasticity neutral?


    2.



    You save 20 000 NOK on a savings account at the end of each year for 9 years. The annual interest rate is 3%.
    a) How much is the total amount immediately after the last deposit?

    b) How much is the total amount 5 years after the last deposit?
    You save an amount K on a savings account at the end of each year for 9 years.The annual interest rate is 3%.

    c) How much is the yearly savings amount if the total amount 5years
    after the last deposit is 300 000?


    3.

    In each of the exercises below, you will see two graphs in the same coordinate system. One is the graph of the function f(x) and the other is the graph of its derivative, f(x). Decide which of the graphs that belongs to f(x) and f(x) respectively. Comment on your answer. You can refer to A and B. It is not necessary to draw the graphs.

    I have attached the A and B .



    Thank you !!!

    Attached Thumbnails Attached Thumbnails S.o.s.-.jpg   S.o.s.-b.jpg  
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  2. #2
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    Quote Originally Posted by Mariana View Post
    ...
    In each of the exercises below, you will see two graphs in the same coordinate system. One is the graph of the function f(x) and the other is the graph of its derivative, f(x). Decide which of the graphs that belongs to f(x) and f(x) respectively. Comment on your answer. You can refer to A and B. It is not necessary to draw the graphs.

    I have attached the A and B .
    [/LEFT]
    Hello, Mariana,

    in both cases it is the best way to compare the zeros of one graph with the properties of the other graph. Then you'll easily see that

    first picture:
    B = f and A = f' because the zeros of A correspond with the local extrema of B

    second picture:
    A = f and B = f' because the zeros of B correspond with the minimum of A

    EB
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