2. A model rocket is launched straight up from ground level with an initial velocity of 96 feet per second. Its height, in feet, after t seconds is given by the equation s(t) =-16t +96t. a. What is the model rocket's maximum height and when in its flight does it reach this point? b. At what time(s) will it reach a height of 80 feet? c. After how many seconds will it return to the ground? Question(s) a., b., and c. should also be answered in sentence form. In addition to showing the calculations that lead to your solution, write a synopsis of the tactic(s) you used to arrive at your solution(s) to this series of questions. Use clear and concise vocabulary, sentence structure, and grammar. Your answer should be labelled with appropriate units and reflect the context used in this question.
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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