Math Calculus

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Let C(x) = 0.02x^3 + 55x^2 + 1380.
Find the minimum average cost for this commodity.

I got to the point where I got x=-1374.98, x=-5.018, x=5

but what do I have to do again after this? Because I am missing some steps after I find x.

Do i have to plug all the X's to the original?

thanks :)

  • You have a typo -

    You have a typo. You need a - sign somewhere on the right.

    dC/dx = 0 at min or max

    .02(3)x^2 + 55(2) x = 0
    x (.06 x + 110 ) = 0
    x = 0 or x = - 1833
    0 or a negative number does not makes sense
    Your cost has no minimum in the first quadrant, it goes up forever with number of units.

  • Math Calculus -

    no i don't see any negative sign in my homework question...

    first I did C*bar(x)/x = 0.02x^3+55x^2+1380/(x)
    = 0.02x^2 + 55 x + 1380/x

    then I differentiate it C*bar*'(x) = 0.4x - 1380/x^2 +55

    then I set it equal to zero which gives me x = -137.317 or x=-5.104 and 4.921

    I did the solve function with the calculator

  • Megan ! - Math Calculus -

    Megan, if you look at your original post, there was no division by x at the end
    So Damon was right to question your typing

    so
    C(x) = (0.02x^3 + 55x^2 + 1380)/x
    = .02x^2 + 55x + 1380/x

    C'(x) = .04x + 55 - 1380/x^2
    = 0 for a max/min of C
    .04x^3 + 55x^2 - 1380 = 0

    solving this with my online equation solver I got
    x = 5 and two negative answers

    so x = 5

    plug that back into original C(x)

  • Math Calculus -

    Reiny,
    Before you do equals to zero, how did you get 0.04x^3 + 55x^2 - 1380 = 0?

    I set
    0.04x + 55 - 1380/x^2 = 0
    and I got x=-137.317, or x=-5.204,, or x=4.921


    if i plus in to the originals i have to plus each x's?

    and the minimum average is the smallest number from the result after I plug in the Xs?

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