Suppose that c (x )equals 4 x cubed minus 16 x squared plus 12 comma 000 x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

Therefore the number of product is 11.42 to minimize the average cost .

Step-by-step explanation:

Given that,

where C(x) is cost of manufacturing of x items.

Differentiating with respect to x

Again differentiating with respect to x

To find the minimum cost, we set C'(x)=0

    [ since 4≠0]

Applying quadratic formula , here a= 3, b= -8, c=-300

      =11.42, -8.76

The number of item is negative, it can't make sense.

∴x=11.42

Now

Therefore when x= 11.42, the cost of manufacturing will minimum.

Therefore the number of product is 11.42 to minimize the average cost .

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct