A. Find the local extrema for the revenue function. ​ B. On which intervals is the graph of the revenue function concave​ upward? Concave​ downward?

Question

A dairy is planning to introduce and promote a new line of organic ice cream. After test marketing the new line in a large city, the marketing research department found that the demand in that city is given approximately by the following equation, where x thousand quarts were sold per week at a price of $p each, and whose revenue function is given as
R(x)equals=xp.

p=9e^-x     0<x<5

Answer 1

You need the first and second derivatives. Set them equal to zero and solve for x numerically using newtons method or bisection method. They cannot be solved explicitly as they contain a mix of x and e^x

 

R''( -1.236 )=0

So for x<-1.236 it is concave

down