A box with a square base and closed top is required to have a volume of 27,000 cm3
. Find the dimensions of the box that minimize the amount of material used.

h=30cm

Base sides, x=30cm

Step-by-step explanation:

Let x be the dimension of the sides and h the dimension of height;

#Material used is directly proportional to surface area. Minimizing surface area will minimize the amount of material used.

Find area as a function of x:

To minimize Area, we find the first derivative of Area:

#find the second derivative to verify the minimum:

Substitute x in the volume equation to find h:

Hence, the dimensions of the box that minimize the amount of material used h=30cm and x=30cm

a

step-by-step explanation:

jjddbdhid r

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).