Minimum average cost
the cost of producing x units of a product is modeled by
c = 500 + 300x - 300 ln x, x ≥ 1.
(a) find the average cost function ć.
(b) find the minimum average cost analytically. use a graphing utility to confirm your result.

a)

b)

Step-by-step explanation:

Given the cost function as C(x):

a) Find the average cost function,

if C is the cost of selling x units, The Average can be denoted by:

this is the average cost function

b) The minimum average cost:

To find the minimum average cost, we'll have to differentiate the average cost function . and equate it to zero. (like finding the stationary point of any function)

now just simplify:

we've found the derivative of C(x), now to find the minimum we'll equate this derivative to zero.

and now solve for x

at this value of x the average cost is minimum.

This is the minimum average cost!

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,