Billy is walking from the front door of his house to his bus stop, which is 940 feet away from his front door. As Billy walks out his front door he walks in a straight path toward his bus stop at a constant rate of 7.5 feet per second.a) Define a function f to determine Billy's distance from his bus stop in terms of the number of seconds he has been walking.b) What is the independent quantity and what is the domain of ff (the values the independent quantity can take on)?c) What is the dependent quantity and what is the range of ff (the values the dependent quantity can take on)?d) What do each of the following represent: f(0) and f(60.25)?e) Use function notation to represent the following: i) Billy's distance from the bus stop after he has walked 23.6 seconds ii) The change in Billy's distance from the bus stop as the number of seconds since Billy left his front door increases from 25 seconds to 48 seconds f) If t represents the number of seconds since Billy left his front door, solve f(t)=150 for t and say what your answer represents.
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.
Billy is walking from the front door of his house to his bus stop, which is 940 feet away from his front door. As Billy walks out his front door he walks in a straight path toward his bus stop at a constant rate of 7.5 feet per second.
a) Define a function f to determine Billy's distance from his bus stop in terms of the number of seconds he has been walking.
b) What is the independent quantity and what is the domain of ff (the values the independent quantity can take on)?
c) What is the dependent quantity and what is the range of ff (the values the dependent quantity can take on)?
d) What do each of the following represent: f(0) and f(60.25)?
e) Use function notation to represent the following:
i) Billy's distance from the bus stop after he has walked 23.6 seconds
ii) The change in Billy's distance from the bus stop as the number of seconds since Billy left his front door increases from 25 seconds to 48 seconds
f) If t represents the number of seconds since Billy left his front door, solve f(t)=150 for t and say what your answer represents.
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