A medical research study tracked the heart rate, in Data from Exercise beats per minute, of a participant engaged in var ious Study Participant types of exercise. The data are graphed on the set of 220- 200 axes below with the time elapsed during the 180 160 observation on the x-axis and the participant's heart * 140 120- 100 80 rate on the y-axis. Based on the graph, which statement is true ? 60 A) The participant's maximum heart rate in the first 40 20 minutes of the observation is about 120 beats 20 per minute. ++x 60 10 20 30 40 50 B) The participant's minimum heart rate is reached Time elapsed (minutes) about 50 minutes after the observation begins. C) The participant's heart rate steadily increases between 25 and 40 minutes during the observation. · D) The participant's resting heart rate is given by the x -intercept of the graph. Heart rate (beats per minute)
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.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
