Suppose we have two functions. One is P(t) , which models the number of photographers entering the park as a function of t , the time in hours since 5 am. The other, F(x) models number of Instagram posts as a function of x , the number of photographers in the park. awe s ! 1 Which composition makes sense: P(F(x)) or F(P(t)) ? And what does this function represent, in the context of the given functions? b) [, soN ti Suppose that P(t) = 19e0.38t models the number of photographers when the time is t hours after 5 am. About what time is it when 120 people are taking pictures in the park? Show your work.
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.
(a) The function P(F(x)) would not make any sense because F(x) s the function 
and it will give result in numbers whereas P(t) is a function of t. Where on the other side the function P(t) will give number of goers which can be put as the variable in F(x). So, F(P(t)) makes sense.
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