Our goal is to use function notation to represent the total fuel cost, in terms of the distance (in miles) of the trip. In doing so we first need to define a function, f, to determine the volume, v, of gasoline used in terms of the distance, d, of a trip. Represent v using function notation. v= Define a function f that determines the volume of gasoline used in terms of the distance, d, (in miles) of a trip. Define a function g that determines the fuel cost, c=g(v), in terms of the volume of gasoline used on the trip.
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.
Our goal is to use function notation to represent the total fuel cost, in terms of the distance (in miles) of the trip. In doing so we first need to define a function, f, to determine the volume, v, of gasoline used in terms of the distance, d, of a trip.
-
Represent v using function notation.
v=
-
Define a function f that determines the volume of gasoline used in terms of the distance, d, (in miles) of a trip.
-
Define a function g that determines the fuel cost, c=g(v), in terms of the volume of gasoline used on the trip.
-
Define a function g that determines the fuel cost, c=g(f(d)), in terms of the volume of gasoline, f(d) used on the trip.
-
Represent the total fuel cost of a 271 mile trip using function notation.
-
Represent the difference in total cost of a 340 mile trip as compared to a 540 mile trip.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
