- #1

tompenny

- 15

- 3

- Homework Statement:
- Determine where a function is strictly increasing/decreasing

- Relevant Equations:
- $$f(x)=x+\frac{1}{(x+1)}$$

Hi there.

I have the following function:

$$f(x)=x+\frac{1}{(x+1)}$$

I've caculated the derivative to:

$$f'(x)=1-\frac{1}{(1+x)^2}$$

And the domain to: $$(-\infty, -1)\cup(-1, \infty)$$

I've also found two extreme point: $$x=0, x=-2$$

I know that a function is strictly increasing if:

$$f'(x)> 0$$

and strictly decreasing if:

$$f'(x)< 0$$

I've calculated the intervalls where the funtcion is strictly increasing to:

$$(-\infty, -2]\cup[0, \infty)$$

and strictly decreasing to:

$$[-2, -1)\cup(-1, 0]$$

My question is if this is correct or if the intervalls should be:

$$(-\infty, -2)\cup(0, \infty)$$ and $$(-2, -1)\cup(-1, 0)$$ instead?

As you can notice I'm very unsecure whether I should use ( or [ at the extremum points?

Any help would be greatly appreciated.

Thank you:)

http://asciimath.org/

http://docs.mathjax.org/en/v1.1-latest/tex.html#supported-latex-commands

I have the following function:

$$f(x)=x+\frac{1}{(x+1)}$$

I've caculated the derivative to:

$$f'(x)=1-\frac{1}{(1+x)^2}$$

And the domain to: $$(-\infty, -1)\cup(-1, \infty)$$

I've also found two extreme point: $$x=0, x=-2$$

I know that a function is strictly increasing if:

$$f'(x)> 0$$

and strictly decreasing if:

$$f'(x)< 0$$

I've calculated the intervalls where the funtcion is strictly increasing to:

$$(-\infty, -2]\cup[0, \infty)$$

and strictly decreasing to:

$$[-2, -1)\cup(-1, 0]$$

My question is if this is correct or if the intervalls should be:

$$(-\infty, -2)\cup(0, \infty)$$ and $$(-2, -1)\cup(-1, 0)$$ instead?

As you can notice I'm very unsecure whether I should use ( or [ at the extremum points?

Any help would be greatly appreciated.

Thank you:)

http://asciimath.org/

http://docs.mathjax.org/en/v1.1-latest/tex.html#supported-latex-commands