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Need help with a calculus question

  • 05-12-2013 01:54AM
    #1
    united2k11
    Registered Users, Registered Users 2 Posts: 245 ✭✭


    A t-shirt manufacturer is planning to expand its workforce. It estimates that the number of t-shirts produced by hiring a new workers is given by:
    T(x) = -0.25^4 + 1x^3 0≤ x≤ 3

    When is the rate of change of T-shirt production increasing, and when is it decreasing?
    (the answer is (0,2) but i need to know how to do the workings for it)

    What is the point of diminishing returns?
    (the answer is x = 2 workers, again i need to know the workings for it)

    What is the maximum rate of change for t-shirt production?
    (answer is 4 ... need to know workings again)

    Thanks for any help. I would appreciate it so much. I am horrible at these types of questions.


Comments

  • #2
    Yakuza
    Registered Users, Registered Users 2 Posts: 5,130 ✭✭✭Yakuza


    Are you sure about that function? Is the first term not missing an x somewhere? As written, it's[latex](\frac{-1}{4})^4 + x^3[/latex] which has no turning point in the range given.

    Assuming you meant [latex]-(\frac{1}{4})x^4 + x^3[/latex], to find where the production starts to decrease, you need to find a point of inflection (http://en.wikipedia.org/wiki/Inflection_point) of that function. To do this, find the second derivative of the above function and set it to zero, then solve the equation. So, in the range of 0 to 3, you will have the turning point of where production starts to decrease.


  • #3
    united2k11
    Registered Users, Registered Users 2 Posts: 245 ✭✭united2k11


    Yakuza wrote: »
    Are you sure about that function? Is the first term not missing an x somewhere? As written, it's[latex](\frac{-1}{4})^4 + x^3[/latex] which has no turning point in the range given.

    Assuming you meant [latex]-(\frac{1}{4})x^4 + x^3[/latex], to find where the production starts to decrease, you need to find a point of inflection (http://en.wikipedia.org/wiki/Inflection_point) of that function. To do this, find the second derivative of the above function and set it to zero, then solve the equation. So, in the range of 0 to 3, you will have the turning point of where production starts to decrease.

    Thanks very much. And yes i forgot the x at -0.25x^4 . thanks!


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