I would recommend that you start by graphing the function of a Ti-83 or higher. If that does not help please post again and I'll try to help more.
Determine the intervals where the function is increasing and where it is decreasing. (Select all that apply.)
Increasing: (e,) (-,e) (-,0) ∪ (e,) (0,) (-,) (-,0) (0,e)
Decreasing: (0,) (-,e) (0,e) (-,0) (-,0) ∪ (e,) (e,) (-,)
Determine the interval(s) where the function f(x) = x2e-x is increasing and where it is decreasing.
Increasing on: (Select all that apply.)
(-, 2) nowhere (-, ) (0, 2) (2, ) (0, )
Decreasing on: (Select all that apply.)
(-, 2) (-, 0) (-, ) nowhere (0, 2) (2, )
Shazzam!!
Cool math .com - Online Graphing Calculator - Graph It!
A graphing calculator for you.
If you have time I would highly recommend downloading WinPlot, it is free and much better.
Answer these questions while looking at the graph for each one:
- Do I have a good picture of this function?
- Where is this function defined?
- Where are the maxima of this function?
- Where is the minima of this function?
- What is the end behavior
- On the left?
- On the right?
The answers to these questions will bring you to your answers.
I have helped you. I have a great deal of work as well, however it is against academic honesty to tell you the answers outright. I strongly recommended that you purchase a graphing calculator asap or discuss this with your teacher.
However, as you do not have a calculator you can use the point at which the derivative of these functions change signs to determine a maximum or minimum according to how the signs change (+ to - versus - to +). You can model the end behavior of logarithmic functions by finding the limits as x approaches zero and x approaches infinity. For the other problem I recommend finding the limits as x approaches positive or negative infinity.
Hello, djdownfawl!
I must assume that you know the basics of derivatives.
. . If is positive, the function is increasing.
. . If is negative, the function is decreasing.
Determine the interval(s) where the function is increasing and where it is decreasing.
. .
First, we note that must be positive.
The derivative is: .
Increasing: we want
We note that the denominator, , is always positive.
So we want: .
Multiply by
Therefore: .
Determine the interval(s) where the function is increasing and where it is decreasing.
. .
The derivative is: .
The denominator is always positive.
The numerator is positive when the two factors are both positive or both negative.
. . Both positive: .
. . . . . . . .Then: .
. . Both negative: .
. . . . . . . . Then: . . . . impossible.
Therefore: .
Teachers expect questions that form part of an assessment that contributes towards the final grade of a student to be the work of that student and not the work of others.
A shame the assignment got locked. Soroban would have got full marks.