• Support PF! Buy your school textbooks, materials and every day products Here!

Example of functions satisfying differentiation properties

  • Thread starter kathrynag
  • Start date
  • #1
598
0
Suppose the function
f has the following four properties:
1. f is continuous for x >=0;

2.
f'(x) exists for x > 0;

3.
f(0) = 0;

4.
f'is monotonically increasing.

I'm just looking for functions that have these 4 properties to better understand what f represents.
So far, I came up with x^2 and x^3, but was looking for more examples. I'm just looking for examples so I can graph these and see a graphical representation. I was getting stuck on good functions to use.
 

Answers and Replies

  • #2
33,182
4,860
Suppose the function
f has the following four properties:
1. f is continuous for x >=0;

2.
f'(x) exists for x > 0;

3.
f(0) = 0;

4.
f'is monotonically increasing.

I'm just looking for functions that have these 4 properties to better understand what f represents.
So far, I came up with x^2 and x^3, but was looking for more examples. I'm just looking for examples so I can graph these and see a graphical representation. I was getting stuck on good functions to use.
How about exponential functions, translated so that they go through the origin? E.g., y = ex - 1.
 
  • #3
598
0
thanks, that makes sense.
 
  • #4
33,182
4,860
Items 3 and 4 say that the graph goes through the origin and is concave up.
 

Related Threads for: Example of functions satisfying differentiation properties

  • Last Post
Replies
1
Views
749
Replies
2
Views
10K
Replies
4
Views
1K
Replies
6
Views
1K
Replies
5
Views
6K
Replies
2
Views
706
Replies
12
Views
2K
Top