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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?

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!

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3 answers

  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

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

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  3. 159.7

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