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Math Help - First derivative, relative extrema questions

  1. #1
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    First derivative, relative extrema questions

    1.) Find the relative maxima and relative minima, if any of the function
    f(x)=sin(x)+cos(x)

    2.)Average cost the average cost in dollars incurred by Records each week in prressing x compact discs is given by

    C(x)=-0.0001x+2+2000/x (0<x<6000)

    Show that C(x) is always decreasing over the interval (0<x<6000)

    3.) Almost half of companies let other firms manage some of their Web operations-a practice called Web hostings .managed services- monitoring
    a customer's technology services is the fastest growing part of Web hosting.
    Managed services sales are expected to grow in accordance with the function.

    f(t)=0.469t^2+0.758t+0.44 (0<t<6)

    measured in billions of dollars and t is measured in years with t=0 corresponding to 1999

    a)find the interval where f is increasing and the interval where f is decreasing.
    b) what does your result tell you about sales in managed services from 1999 through 2005?
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  2. #2
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    Quote Originally Posted by lemontea View Post
    1.) Find the relative maxima and relative minima, if any of the function
    f(x)=sin(x)+cos(x)

    Mr F says: Solve f'(x) = 0 and test the nature of the solutions.

    2.)Average cost the average cost in dollars incurred by Records each week in prressing x compact discs is given by

    C(x)=-0.0001x+2+2000/x (0<x<6000)

    Show that C(x) is always decreasing over the interval (0<x<6000)

    Mr F says: Show that C'(x) < 0 over the given interval.

    3.) Almost half of companies let other firms manage some of their Web operations-a practice called Web hostings .managed services- monitoring
    a customer's technology services is the fastest growing part of Web hosting.
    Managed services sales are expected to grow in accordance with the function.

    f(t)=0.469t^2+0.758t+0.44 (0<t<6)

    measured in billions of dollars and t is measured in years with t=0 corresponding to 1999

    a)find the interval where f is increasing and the interval where f is decreasing.

    Mr F says: Solve f'(t) > 0 and f'(t) < 0 respectively.

    b) what does your result tell you about sales in managed services from 1999 through 2005?

    Mr F says: Interpret your solutions to (a).
    ..
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  3. #3
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    >< i still dont know how to do it
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  4. #4
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    Quote Originally Posted by lemontea View Post
    >< i still dont know how to do it
    Do you know how to differentiate?

    Do you know how to solve equations and inequations?

    Show all your working and state where you get stuck.
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  5. #5
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    Lemontea, simply find the first derivative and find the zeros of the first derivative. The point at which the derivative is zero are common points for extrema.

    You need to use a line graph to check whether it's increasing/decreasing.
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