Question

The cost C of producing x units of a product is given by C= (.2(x^2)+10x+5) and the average cost per unit is given by (.2(x^2)+10x+5)/x where x>0. Sketch the graph of the average cost function and estimate the number of units that should be produced to minimize the average cost per unit

Answer 1

I already sketched the graph

Answer 2

Have you learned derivatives

Answer 3

and I don't know how to find the number of units that should be produced to minimize the average cost

Answer 4

I have not learned derivatives

Answer 5

Im in precalc

Answer 6

Okay so you learned limits right?

Answer 7

yes, I have

Answer 8

I mean we learned what they are but didn't learn how to do them
xD

Answer 9

wait a second I'm wrong somewhere ignore me xd

Answer 10

Your graph is like this
https://www.desmos.com/calculator/pgeuedi06p

Answer 11

okay let's see

Answer 12

Using my eye, it looks like it's right at 5. Doesn't it?

Answer 13

btw a derivative is kinda like this:

\[(a)(x^b) \rightarrow (ab)(x^{b-1})\]

and that's the slope function. If you try to solve for when it equals to 0 (cause that's the minimum) then you got your answer.

Are you still there?

Answer 14

I doubt we need to know derivatives because that is a calc skill

Answer 15

we learned how to do slant asymptotes, do you think that has anything to do with this problem

Answer 16

it says to just sketch and estimate, so there's no need for any math unless I'm wrong. I couldn't think of a way to solve this without calculus either so just look for the point that is reasonable (because it is a real-world scenario) and see the minimum for the Avg. cost per unit