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Math Help - Quotient Rule - overall max value of function

  1. #1
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    Quotient Rule - overall max value of function

    Hi,

    I'm stuck on this and would be grateful for any help.

    I need to find the overall maximum value (correct to two decimal placeds) of the function:

    f(x) = 20x / 5 + x^2

    on the interval (0, 6)

    Please help, I don't know how to go about doing this!
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  2. #2
    Senior Member
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    Hello buddy.

    Quote Originally Posted by looking0glass View Post
    Hi,

    I'm stuck on this and would be grateful for any help.

    I need to find the overall maximum value (correct to two decimal placeds) of the function:

    f(x) = 20x / 5 + x^2

    on the interval (0, 6)

    Please help, I don't know how to go about doing this!
    You do! You already know you must use the quotient rule. Why is that? Because if you want to find the critical points of a function f(x), you need to consider the derivative : f'(x)

    Finding f'(x) - use quotient rule

    f'(x) = \frac{20*(5+x^2)-2x*20x}{(5+x)^2} = \frac{20(5 - x^2)}{(x^2 + 5)^2}

    To find the critical points solve

    f'(x) = 0. Thus

     \frac{20(5 - x^2)}{(x^2 + 5)^2} = 0

    multiply by (x^2+5)

    20(5-x^2) = 0

    <=> 5-x^2 = 0

    and then you find x_E.

    To show that it is a max, solve f''(x_E); f''(x_E) must be < 0

    To find the y-coordinate of your critical point, you need to solve f(x_E)

    Yours
    Rapha
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  3. #3
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    Hi thanks!

    Is the answer 4.47?
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  4. #4
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    Hey

    Quote Originally Posted by looking0glass View Post
    Hi thanks!

    Is the answer 4.47?
    You're welcolme.

    Yep! The critical point is  (\sqrt{5} \ , \ 4.47), so you are correct..
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