INCREASE AND DECREASE. EXERCISES
Analysis
 

3. APPLICATIONS
1) Find the intervals of increase and decrease of the function f(x)=x4-2x2

Complete the following first in your exercise book:

  • Find f'(x) and solve the equation: f'(x)=0

  • Find the sign of the derivative on either side of these values

  • Write down the intervals of increase and decrease

In the top part of the window make the value of the DERIVATIVE equal to 1. The graph of  f'(x) will appear.

At which points does the function cut the X-axis? What is the sign on either side of these points?

Change the value of x and f will appear so that you can check your results.

 
2) The industrial production of a country is represented by the function f(x)=3/(1+e-x) where x is the number of years since 2000. Is production growing or decreasing?

As before:

  • Find f'(x). What is the sign for the value x=present year-2000?

  • Is production increasing or decreasing?

  • Check the situation for other years.

In the top part of the window make the value of the DERIVATIVE equal to 1. The graph of  f'(x) will appear.

  • Does this function cut the X-axis? What is the sign of the function over its whole domain?

Change the value of x and f will appear so that you can see its behaviour and check your results.
 
3) The temperature in a city on New Year's Day has the formula f(x)=-x(x-26)/13 where x is the number of hours after midnight. When does the temperature drop during the day?

As in the two examples above:

  • Find f'(x) and solve the equation: f'(x)=0

  • From which value is f'(x)<0?

  • What was the temperature just before it started to drop?

In the top part of the window make the value of the DERIVATIVE equal to 1. The graph of  f'(x) will appear.

  • Where does this function cut the X-axis? For which values of x is it negative?

As above, change the value of x and f will appear so that you can check your results.

       
           
  María José García Cebrian
 
Spanish Ministry of Education. Year 2001
 
 

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