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# first derivative and second derivative

Please see the attached file (word problems, inflection, critical points, and derivatives)

14. You run a small furniture business. You sign a deal with a customer to deliver up to 400 chairs, the exact number to be determined by the customer later. The price will be \$90 per chair up to 300 chairs, and above 300, the price will be reduced by \$0.25 per chair (on the whole order) for every additional chair over 300 ordered. What are the largest and smallest revenues your company can make under this deal?

For each of the functions in problem 4-8, do the following:
(a) find f' and f''
(b) find the critical points of f.
(c) find any inflection points of f.
(d) evaluate f at its critical points and at the endpoints of the given interval. Identify local and global maxima and minima of f in the interval.
(e) graph f.

#### Solution Summary

The solution is a detailed guide on first derivative and second derivative of functions. It also includes an application dealing with the maximum and minimum revenue of a furniture business.

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