Posted by Megan on .
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 
Damon,
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 
Megan,
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 
Reiny,
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 
Megan,
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?