Goro Shigeno (Pitcher) and Joe Gibson Jr. (hitter) went head to head in the Major League Baseball (MLB) series. For the last pitch, Gibson hits the baseball with 82 ft/s at angle of 75o
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.
Goro Shigeno (Pitcher) and Joe Gibson Jr. (hitter) went head to head in the Major League Baseball (MLB)
series. For the last pitch, Gibson hits the baseball with 82 ft/s at angle of 75o
. When the ball is directly
above Shigeno he begins to run under it. Determine the (a) the total distance that the pitcher runs and (b)
the constant speed at which pitcher must run in order to make the catch at the same elevation at which
the ball was hit. (Note: the distance between the pitcher and hitter is 70 ft.
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