Question: Businesses are always looking at ways to improve profits or maximize profits. As we have seen in Unit 1 that profit is the difference between revenue and cost, i.e.

Profit \[\pi \] ( q)= R(q) – C(q)

The marginal cost is the derivative of the cost function and marginal revenue is the derivative of the revenue function, i.e.,

MC = \[C'\left( q \right)\] and MR = \[R'\left( q \right)\]

Global maxima and minima of a function can occur at critical points of the function or at the endpoints of the interval. To find out the critical points of profit function \(\pi \) we find the derivatives and equate to zero, i.e.,

\[\pi '\left( q \right)=R'\left( q \right)-C'\left( q \right)\]

\[R'\left( q \right)=C'\left( q \right)\]

1. Suppose the graph in Figure 4.1.78 is that of a function g(x) , -1 \(\le \) x \(\le \) 2 . Sketch the graph of the derivative \(g'\left( x \right)\)
   
2. On the other hand, suppose the graph above is that of the derivative \(f'\)

of a function f . For the interval \(1\le \)  x \(\le \) 2 , tell where the function f is

1. increasing;
2. decreasing.
3. Tell whether f has any extrema, and if so, where they are.

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Solution: The downloadable solution consists of 2 pages
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