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Derivative Applications of Calculus Graphs

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1) determine the interval(s) where the function is increasing and the interval(s) where it is decreasing.

2) determine the interval(s) where the function is increasing and the interval(s) where it is decreasing.

3) Find the relative maxima and relative minima, if any, of the following function. Show your work and the procedure.

4) Suppose the total cost function for manufacturing a certain product is dollars, where x represents the number of units produced. Find the level of production that will minimize the average cost

5) The weekly demand for the Pulsar 25 color console television is --- where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly cost function is given by --- where denotes the total cost incurred in producing x sets.

a) Find the revenue function R and the profit function P.
b) Find the marginal cost function , the marginal revenue function , and the marginal profit function .
c) Compute R' and C' (2000)Interpret each of these values.

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This provides examples of using derivatives to determine intervals of increase and decrease, extrema, and minimization.

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