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The cost, in dollars, of producing x balls is given by C(x)=714+10x−0
The cost, in dollars, of producing x balls is given by C(x)=714+10x−0.078x2C(x)=714+10x−0.078x2. Find the rate at which average cost is changing when 676 balls have been produced.
When 676 balls have been produced, the produced, the average cost is changing at _____ for each additional belt.
Expert Solution
Given cost function c(x)=714+10x−0.078x2c(x)=714+10x−0.078x2.
The average cost function is :
ca(x)=714x+10−0.078x.ca(x)=714x+10−0.078x.
Rate of change of average cost is:
c′a(x)=−714x2−0.078ca′(x)=−714x2−0.078
Rate of change of average when x=676x=676 is:
c′a(676)=−7146762−0.078=−0.00156−0.078=0.07956
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