The cost of producing x units of a certain commodity is C(x)=1000+5.70x+0.7x^2 . What is the average rate of change of C with respect to x when the production level is raised from x = 100 to x = 120 and when the production level is raised from x = 100 to x = 101?

Question

I'm trying very hard to understand this but I'm missing some steps somewhere. If anyone could walk me through this process I would be much obliged.

I know I'm supposed to use a formula like [C(120) - C(100)] / [120 - 100] but I'm not sure what to input for C or what to do afterwards. Thanks!

Answer 1

cost to produce 120 units
= C(120) = 1000+5.7(120) + .7(120^2) =
= 11764
cost to produce 100 units = C(100)
= 8570

rate of change = (11764-8570)/(120-100)
= 3194/20
= 159.70 dollars/unit

repeat the process for 100 to 101

Answer 2

THANK YOU oh my goodness, that was so simple I can't believe I missed that. Thanks a bunch. That makes perfect sense.

Answer 3

159.7