Target Heart Rate Ranges for Exercise Goals Exercise Goal Boost performance as a competitive sthlete Improve cardiovaseular conditioning Lose weight Improve overall health and PHA reduce risk of heart attack 그 4 5 1 10 10 Fraction of Maximum Heart Rate, 220 – a lin
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.
The maximum heart rate, in beats per minute, that you shouldachieve during exercise is 220 minus your age, 220 - a, where 'a' is the age.
The bar graph shows the target heart rate ranges for four types of exercise goals. The lower and upper limits of these ranges are fractions of the maximum heart rate, 220 - a.
If your exercise goal is to improve cardiovascular conditioning, the graph shows the following range for target heart rate, H, in beats per minute, for lower limit of range H = 7/10 (220 − a), for upper limit of range H = 4/5 (220 − a).
Solve, a. What is the lower limit of the heart rate range, in beats per minute, for a 20-year-old with this exercise goal?
b. What is the upper limit of the heart rate range, in beats per minute, for a 20-year-old with this exercise goal?
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