# The meaning of U ' ( t ) and also the unit of U ' ( t ) . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.7, Problem 33E

a.

To determine

## The meaning of U'(t) and also the unit of U'(t) .

Expert Solution

### Explanation of Solution

Given information:

The unemployment rate U(t) varies with time.

The table gives the percentage of unemployed in US labor force from 1998 to 2007

 t U(t) t U(t) 1998 4.5 2003 6.0 1999 4.2 2004 5.5 2000 4.0 2005 5.1 2001 4.7 2006 4.6 2002 5.8 2007 4.6

Calculations:

Here U'(t) shows the slope of the tangent of the curve made by the function or rate of change of unemployed with respect to time (in years) . The unit of U'(t) will be Unemployed peer year.

The slope of the tangent is given the formula,

f'(x)=limh0f(x+h)f(x)h

b.

To determine

Expert Solution

### Explanation of Solution

Given information:

The unemployment rate U(t) varies with time.

The table gives the percentage of unemployed in US labor force from 1998 to 2007

 t U(t) t U(t) 1998 4.5 2003 6.0 1999 4.2 2004 5.5 2000 4.0 2005 5.1 2001 4.7 2006 4.6 2002 5.8 2007 4.6

Calculations:

Here U'(t) shows the slope of the tangent of the curve made by the function or rate of change of unemployed with respect to time (in years) . The unit of U'(t) will be Unemployed peer year.

The slope of the tangent is given the formula,

f'(x)=limh0f(x+h)f(x)h

 t U(t) U'(t) t U(t) 1998 4.5 2003 6.0 0.2 1999 4.2 -0.3 2004 5.5 -0.5 2000 4.0 -0.2 2005 5.1 -0.4 2001 4.7 0.7 2006 4.6 -0.5 2002 5.8 1.1 2007 4.6 0

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