Part I: Derivatives Graphically A small company produces hand-stitched backpacks. The company finance team provides the...

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Part I: Derivatives Graphically A small company produces hand-stitched backpacks. The company finance team provides the following plots which represent the monthly revenue, R(x), and cost, C(x), of producing x backpacks each month. The company wants to know what monthly production quantity will maximize their profit. 1. (a) Sketch the tangent lines of C(x) and R(x) at x = 400 in the figure to the right and label each line. (b) Use the tangent lines to estimate C'(400) and R'(400). (Recall the slope of the tangent line of a function at a point is the value of the derivative of the function at that point) Dollars 120,000 C(x) - R(x) 100,000 80,000 60,000 40,000 20,000 0 0 200 400 600 800 1,000 1,200 1,400 Number of backpacks produced monthly 2. Why are your answers to 1(b) approximations and not exact answers? Explain. Part I: Derivatives Graphically A small company produces hand-stitched backpacks. The company finance team provides the following plots which represent the monthly revenue, R(x), and cost, C(x), of producing x backpacks each month. The company wants to know what monthly production quantity will maximize their profit. 1. (a) Sketch the tangent lines of C(x) and R(x) at x = 400 in the figure to the right and label each line. (b) Use the tangent lines to estimate C'(400) and R'(400). (Recall the slope of the tangent line of a function at a point is the value of the derivative of the function at that point) Dollars 120,000 C(x) - R(x) 100,000 80,000 60,000 40,000 20,000 0 0 200 400 600 800 1,000 1,200 1,400 Number of backpacks produced monthly 2. Why are your answers to 1(b) approximations and not exact answers? Explain.