Describing the closed interval and determining the function values The range R of the projectile fired from the origin over horizontal ground is the distance from the origin to the point of impact. If the projectile is fired with an initial velocity of v, at an angle a with the horizontal, then R= · 2 sin(a) cos(a) where g is the downward acceleration due to gravity. Using a slingshot, Danny George, of the UK, fired a 3/8- inch projectile at a speed of 654 feet per second. This is a Guinness World Record and so we know it took place here on planet Earth where downward acceleration due to gravity is g= 32.17 , sec? We want to determine what angle a Danny George should have used to maximize the range of the projectile and what the greatest range that can be achieved is. Create a table of function values for R that includes the Over what closed interval of angles are you trying to find the maximum range? endpoints of your closed interval and any critical numbers that are in the closed interval. olnho
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.
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