A store has issued two different coupons for its customers to use. One coupon gives customers $20 off their purchase price, and the other coupon gives customers 20% off of their purchase. The store allows customers to use both coupons and choose which coupon to apply first. For this context, ignore sales tax. Let D be the function that inputs a cost (in dollars) and outputs the cost after applying the "$20 off" coupon, and let P be the function that inputs a cost (in dollars) and outputs the cost after applying the "20% off" coupon. a. A customer purchases an item for $110 and asks the cashier to apply the "$20 off" coupon first, followed by the "20% off" coupon. What is the cost of the item after the two coupons are applied? $ 72 Preview b. A customer purchases an item for $110 and asks the cashier to apply the "$20 off" coupon first, followed by the "20% off" coupon. Use function notation to represent the cost of the item (in dollars) after the two coupons are applied. Preview syntax error c. A customer purchase an item for $110 and asks the cashier to apply the "20% off" coupon first, followed by the "$20 off" coupon. What is the cost of the item after the two coupons are applied? $ 68 Preview d. A customer purchases an item for $110 and asks the cashier to apply the "20% off" coupon first, followed by the "$20 off" coupon. Use function notation to represent the cost of the item (in dollars) after the two coupons are applied. Preview

Q: determine and correctly interpret the maximum or minimum of the functions that model the following…

A:

Q: The average cost per set for the production of television sets is given by 810+10x+0.1x² C(x)= where…

A:

Q: + 4 2+ 4 y = 0 with y(0) = 1.5 and d²y dy dy (0) = 0 dt² dt dt

A: Given initial valve problem is: d2ydt2+4dydt+4y=0  ⋯⋯1 with  initial conditions y0=1.5 and dydt0=0…

Q: Suppose that a company has just purchased a new computer for $2400. The company chooses to…

A:

Q: Graph the function y=-1.765x2 + 40.165x + 389.755 for x-values between 1 and 10.  Determine the…

A: We have to calculate the values of "y" by applying the values of "x".

Q: A downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that.…

A: The charges are $5 per hour for the first two hours. The charges are $2.5 per hour after the first…

Q: portable TV’s has fixed costs of $325 and variable costs of $55 per TV. Let x be the total number of…

A: We  will solve first find the revenue function,  profit function and then find number of sales for…

Q: A devastating freeze in California's Central Valley in Sanugry fHhe state's out approximately 75% of…

A: The given question should be converted into a linear equation using the given conditions.  Then we…

Q: 14. A single pump is filling a storage container with water at a rate of 60 gallons per minute.…

A: Given data:   The volume of water in the container is V0=1,500 gallons The rate at which a single…

Q: A downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that.…

A:

Q: What would the revenue function be

A: As we see Demand function Dx=-0.095x+4.545

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.