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Math Help - [urgent]calculus Questions

  1. #1
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    [urgent]calculus Questions

    i need answers by 11:50 pm today:

    1. Let f(t)=7cos^2(5t) where domain= t is between -pi/5 and pi/5.

    a)Find all (open) intervals on which f(t) is increasing and concave up.

    b)Decreasing and concave up

    c)Increasing and concave down

    d)decreasing and concave down

    e)List all t values where f(t) has inflection points, in increasing order.

    f)List the values of the function f(t) corresponding to the inflection points

    I) List the values of the slopes of the tangent lines at the inflection points



    4. A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 7-x^2. What are the dimensions of such a rectangle with the greatest possible area?

    Width=? Height=?



    6. A farmer wishes to fence off two identical adjoining rectangular pens, each with 600 feet of area, as shown.


    where are x and y so that the least amount of fence is required.
    x= ? feet y= ? feet


    *Answers would be great. But if you just want to give me a thorough guidance how to do any of the problems, POST PLEASE!
    Last edited by methlover; March 7th 2008 at 07:21 PM.
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    Quote Originally Posted by methlover View Post
    i need answers by 11:50 pm today:

    1. Let f(t)=7cos^2(5t) where domain= t is between -pi/5 and pi/5.

    a)Find all (open) intervals on which f(t) is increasing and concave up.

    b)Decreasing and concave up

    c)Increasing and concave down

    d)decreasing and concave down

    e)List all t values where f(t) has inflection points, in increasing order.

    f)List the values of the function f(t) corresponding to the inflection points

    I) List the values of the slopes of the tangent lines at the inflection points

    [snip]
    You need to do two things:

    1. Draw a graph.

    2. Solve f''(t) = 0.

    These two things plus a small amount of thought should enable you to answer all of the above questions.
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    Quote Originally Posted by methlover View Post
    i need answers by 11:50 pm today:

    [snip]
    4. A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 7-x^2. What are the dimensions of such a rectangle with the greatest possible area?

    Width=? Height=?

    [snip]
    Let the lower corners be at (-x, 0) and (x, 0). Then the width is 2x and the height is y = 7 - x^2. So the area is A = 2x(7 - x^2). Use calculus to find the x-coordinate of the maximum turning point of A. The required dimensions follow from the value of this x-coordinate.
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    Quote Originally Posted by methlover View Post
    i need answers by 11:50 pm today:

    [snip]6. A farmer wishes to fence off two identical adjoining rectangular pens, each with 600 feet of area, as shown.


    where are x and y so that the least amount of fence is required.
    x= ? feet y= ? feet

    [snip]
    xy = 600 .... (1)

    Length of fencing = L = 3y + 4x .... (2)

    Using (1) and (2):

    L = \frac{1800}{x} + 4x.

    Use calculus to find the x-coordinate of the minimum turning point of L. The required values of x and y follow from the value of this x-coordinate.
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