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The unemployment rate $ U(t) $ varies with time. The table gives the percentage of unemployed in the US labor force from 2003 to 2012.

(a) What is the meaning of $ U'(t) $? What are its units?

(b) Construct a table of estimated values for $ U'(t) $.

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Campbell University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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The table below lists the …

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this phone number thirty five of this tour Calculus eighth edition Section two point eight The unemployment rate U of t varies with time. The table gives the percentage of unemployed in the US labor force from two thousand three to two thousand twelve. What is the meaning out You prime a team water its unit. So here we see the unemployment rate in percent of people unemployed. Ah, percent of people with district of the full population. That's the U. And we have that data for every year from two thousand three two thousand twelve. You promised he would be the derivative of you with respect to temper our two time so two year and therefore you promised. He represents the change in the unemployment rate. Ah, per year and it's units are percent of people unemployed her year. So we can definitely write that here Percent of people unemployed him, uh, per year. All right are being contract the table of estimated values for you prime of team. But here's an attempt at estimating the values of you. Prime Minister. Here's an example of what is being done for this here two thousand four. We're taking the average uh, the ray of change from two thousand three to two thousand four and the rate of change between two thousand four two thousand five. So essentially we were gonna have the next year, minus the first year, the change in the unemployment rate to bed about it one year on DH. That's one average rate of change. And then we're going to do that because here. So the unemployment rate, her the unemployment percent, someone here and then the reform, that difference of the unemployment rate to everybody. One air, which is the interval. And those two average rate of change is are averaged for each of the years and against us thes approximate rates of change for you, prime of team and at the end points. Since there's no information for before or after, then it's just are given as thie average sort of change with the data given from the year before or from the hereafter. So these air the estimates that we have come up with for the average or for the rate of change over the unemployment rate, uh, with respect to time per year,

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