(Solved): For the function, locate any absolute extreme points over the given interval. (Round If an answer d ...

For the function, locate any absolute extreme points over the given interval. (Round If an answer does not exist, enter DNE.) \[ g(x)=-3 x^{2}+14.7 x-16.1,-1 \leq x \leq 5 \] absolute maximum \( (x, y)=(14,1 x-10.1,-1 \leq x \leq 5) \) absolute minimum \( (x, y)= \) street vendor constructs the table below on the basis of sales data. (Note: Consumer expenditure and revenue are term the same thing from different perspectives. Consumer expenditure is the amount of money that consumers spend on oduct, and revenue is the amount of money that businesses take in by selling the product.) Sales of Roses, Given the Price ner Davan (a) Find a quadratic function for the model of the data that gives the quantity sold at \( x \) dollars, data from \( 20 \leq x \leq 32 \). (Round all numerical values to three decimal places.) \( S(x)= \) (b) Find a function for the model for consumer expenditure (revenue for the vendor), where \( x \) is the price in dollars data fromt \( 20 \leq x \leq 32 \). (Round all numerical values to three decimal places.) \( R(x)= \) (c) What price should the street vendor charge to maximize consumer expenditure? (Round your answer to two decimal places.) (d) If each dozen roses costs the vendor \( \$ 13 \), what price should he charge to maximize his profit? (Round your answer to two decimal places.)