# function concave

• Feb 12th 2009, 11:29 AM
FionaG
function concave
I'm sorry about my bad English, because I don't know the right expression for this, but I hope that you'll understand what I mean.
What are the X's "values" which will make the following function "dwindling" f(X)=(2X-1)(X+3) I really hope that someone understands what I mean and can help me too. Thank you very very much.
• Feb 12th 2009, 11:36 AM
running-gag
Hi

Do you mean decreasing ?
Such as for x < y, f(x) > f(y)
• Feb 12th 2009, 12:22 PM
Soroban
Hello, Fiona!

I'll take a guess at what you meant . . .

Quote:

For for what $x$-values is: $f(x) \:=\:\frac{2x-1}{x+3}$ a decreasing function?

If we are allowed to use Calculus, determine when $f'(x) \,<\,0.$

We have: . $f\:\!'(x) \:=\:\frac{2\cdot(x+3) - (2x-1)\cdot1}{(x+3)^2} \;=\;\frac{7}{(x+3)^2}$

And we see that $f\:\!'(x)$ is always positive.

The function is never decreasing.

The graph is even more convincing . . .
Code:

                  *:      |                     :      |                   * :      |                 *  :      |               *    :      |             *      :      |       *            :      |2     - - - - - - - - + - - - + - - - - - - -                     :      |            *  -------------------+-------+-----*------------                   -3:      *                     :  *  |                     : *    |                     :      |                     :*      |                     :      |