# POLYNOMIAN AND RATIONAL FUNCTIONSSeveral popular models of carry-on luggage have a length 10 in greater than their depth to comply with airline regulations, the sum of the length, width, and depth may not exceed 40 in.a.1. Assume the sum of the length, width, and depth is 40 in. Graph the function relating volume V to depth x.a.2. Find the x-intercepts.a.3. What do they represent?a.4. Relate Volume = ?b. Describe a realistic domainc.1. What is the maximum possible volume of a piece of luggage?c.2. What are the corresponding dimensions of the luggage? c.3. Look for the greatest value of y that occurs within the domain 0, x, 15.C.4. Use the maximum feature of a graphing calculator to find the maximum value.

Question

POLYNOMIAN AND RATIONAL FUNCTIONS

Several popular models of carry-on luggage have a length 10 in greater than their depth to comply with airline regulations, the sum of the length, width, and depth may not exceed 40 in.

a.1. Assume the sum of the length, width, and depth is 40 in. Graph the function relating volume V to depth x.

a.2. Find the x-intercepts.

a.3. What do they represent?

a.4. Relate Volume = ?

b. Describe a realistic domain

c.1. What is the maximum possible volume of a piece of luggage?

c.2. What are the corresponding dimensions of the luggage?

c.3. Look for the greatest value of y that occurs within the domain 0, x, 15.

C.4. Use the maximum feature of a graphing calculator to find the maximum value.

Step 1

As per norms, (only) the first three sub-parts are answered.

The problem is concerned with the properties of the function V(x), as defined in the question

Step 2

Convert the given data into equations. Let l ,w , x represent the length , width and the depth (=x) of the model and let V  represent the volume of the luggage. V(x) = -2x^3+10x^2+300x (explicitly as a polynomial function of x)

Step 3

a1) The graph of y=V(x). Because of the large value...

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