Average and marginal cost Consider the following cost functions. a. Find the average cost and marginal cost functions. b. Determine the average cost and the marginal cost when x=a. c. Interpret the values obtained in part (b). C(x)=−0.04×2+100x+800,0≤x≤1000,a=500

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Average and marginal cost Consider the following cost functions.  a. Find the average cost and marginal cost functions.  b. Determine the average cost and the marginal cost when x=a.  c. Interpret the values obtained in part (b). C(x)=−0.04×2+100x+800,0≤x≤1000,a=500

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Step 1 GivenC(x)=−0.04×2+100x+800,0≤x≤1000,a=500a) Find average costAverage cost a(x)=c(x)xa(x)=−0.04x2+100x+800xMarginal cost function =a′(x)a‘(x)=ddx(−0.04x2+100x+800x)Apply the quotient rule here and find the derivative(fg)‘=f‘g−g‘fg2=x(2(−0.04x)+100)−1(−0.04x2+100x+800)x2=−0.08x2+100x+0.04x2−100x−800x2=−0.04x2−800x2Step 2 The average cost and the marginal cost when x=aa(x)=−0.04x2+100x+800xNow a=500 plug in a(x)a(500)=−0.04(500)2+(500)+800500=−0.04(250,000)+50,000+800500=40800500a(500)=81.6Now we need to find a&#039;(500)a‘(500)=(−0.04(500)2−8005002)=−0.04(250,000)−800250,000=−10,800250,000a‘(500)=−0.0432c) marginal cost decreases

Average and marginal cost Consider the following cost functions. a

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