6.5: Relative Maxima, Relative Minima, Zeros
- Author:
- Eric Soha
The objective of this lesson is for you to be able to identify relative maxima, relative minima, and the zeros of functions by analyzing graphs and tables. You will be analyzing three different functions to answer the questions below. Here is a brief description of the functions and how you should manipulate and analyze them.
f(x): Use the slider to observe how f(x) changes as x changes (note that a=x).
g(x): Use first two columns in the table to analyze g(x).
h(x): In the table, cell C2 shows the value of h(a) as you manipulate the slider. As of right now, you can see that h(-6)=447.83.1. As you change "a", h(x) will change (again, note that a=x).
*Please do not check off "Show g(x)" or "Show h(x)" until you are instructed to do so.
Problem Set 1: Use the red slider and "Show f(x)" checked on
1. At what value of x does f(x) have a relative maximum?
a. For this value, make a small table for f(x-1), f(x), and f(x+1).
b. What do you notice about the values in the table? How might it help you find relative maxima in a table?
2. At what value of x does f(x) have a relative minimum?
a. For this value, make a small table for f(x-1), f(x), and f(x+1).
b. What do you notice about the values in the table? How might it help you find relative minima in a table?
3. At what values of x does f(x) have zeros?
a. Yeah...by now...you get it...
b. Mhmm...you know what to do...
Problem Set 2: Analyze g(x) by looking at the first two columns in the table
1. Use what you learned from Problem Set 1 to help you identify all the...
a. Relative maxima.
b. Relative minima.
c. Zeros.
2. When you are finished, check off, "Show g(x)" to see how you did.
Problem Set 3:Use the slider to change the value of h(a), which you can find in cell C2
1. Use what you have learned to find all the relative max., relative min., and zeros.
2. When you think you have them all, check off "Show h(a)" and use the slider to see what the function really looks like. Note: h(a) is a single green point.