Suppose the height of a firework shell in feet can be modeled by the equation H(t)=-50t^2+450t where t is the time in seconds since ignition a)Complete the table of values and Sketch the graph (Label the axis with words) b) What is the domain and range of the function in the context of this problem situation (relative domain and range)? c)What is the abstract domain and range of the function - not in the context of this problem situation? d) Find and interpret H(8)

Q: + 4 2+ 4 y = 0 with y(0) = 1.5 and d²y dy dy (0) = 0 dt² dt dt

A: Given initial valve problem is: d2ydt2+4dydt+4y=0  ⋯⋯1 with  initial conditions y0=1.5 and dydt0=0…

Q: Can a function also be pictured as an arrow diagram?

A: Yes, a function can be pictured as an arrow diagram. To picture a function as an arrow diagram the…

Q: What is the domain and range of y= 2-x Is it a function?     Please provide solution thanks!

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Q: Consider the equation y=x^3-16x^2+2x-4 a. Determine all intervals over which the graph is concave…

A: For a function y = f( x ) For concave up f''( x ) > 0 For concave down f''( x ) < 0  Given…

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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.