1. ## 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.

2. Hi

Do you mean decreasing ?
Such as for x < y, f(x) > f(y)

3. Hello, Fiona!

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

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

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

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

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

The function is never decreasing.

The graph is even more convincing . . .
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