Taxi Miles The Inner City Taxi Company estimated,on the basis of collected data, that the number of taximiles driven each day can be modeled by the function Q = 489L0.6, when they employ L drivers perday.a. Graph this function for 0 <= L <= 35.b. How many taxi miles are driven each day if thereare 32 drivers employed?c. Does this model indicate that the number of taximiles increases or decreases as the number ofdrivers increases? Is this reasonable?d. Is the graph of this function concave up or concavedown? What does this mean?
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.
Taxi Miles The Inner City Taxi Company estimated,
on the basis of collected data, that the number of taxi
miles driven each day can be modeled by the function Q = 489L0.6, when they employ L drivers per
day.
a. Graph this function for 0 <= L <= 35.
b. How many taxi miles are driven each day if there
are 32 drivers employed?
c. Does this model indicate that the number of taxi
miles increases or decreases as the number of
drivers increases? Is this reasonable?
d. Is the graph of this function concave up or concave
down? What does this mean?
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