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 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.
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, 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)
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?
After finding the values of x as -1374.98, -5.018, and 5, you need to evaluate the average cost function C(x) at each of these values and determine the minimum value. To do this, you will substitute each value of x back into the original equation C(x) = 0.02x^3 + 55x^2 + 1380.
Plug in x = -1374.98:
C(-1374.98) = 0.02(-1374.98)^3 + 55(-1374.98)^2 + 1380
Plug in x = -5.018:
C(-5.018) = 0.02(-5.018)^3 + 55(-5.018)^2 + 1380
Plug in x = 5:
C(5) = 0.02(5)^3 + 55(5)^2 + 1380
Evaluate the function at each x-value using a calculator or computer program and find the minimum average cost among the three values obtained. The x-value that corresponds to this minimum average cost will be the answer.
Remember to pay attention to the units and context of the problem regarding the cost and x-values.