findind the absolute

[dear2009]

Dear Math Help participants

The absolute minimum of

see below Image

over the interval [0, 1] occurs at x=?

Any help would be greatly appreciated. Thanks in advance.

 

[Deleted member 4993]

Dear Math Help participants

The absolute minimum of

see below Image

over the interval [0, 1] occurs at x=?

Any help would be greatly appreciated. Thanks in advance.

First plot your function and observe the absolute minimum within the given domain.

How much is it? where (x) is it?

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[BigGlenntheHeavy]

$\displaystyle f(x) \ = \ x+1+\frac{5}{x+2}, \ f \ ' \ (x) \ = \ 1-\frac{5}{(x+2)^{2}} \ = \ \frac{x^{2}+4x-1}{(x+2)^{2}}$

$\displaystyle Setting \ the \ slope \ = \ to \ zero, \ we \ have \ x \ = \ \sqrt5-2, \ over \ the \ interval \ [0,1].$

$\displaystyle Hence, \ f(\sqrt5-2) \ = \ 2\sqrt5-1, \ thus \ min. \ point \ = \ (\sqrt5-2,2\sqrt5-1).$

$\displaystyle Question: \ What \ are \ the \ equations \ for \ the \ two \ asymptotes \ of \ f(x) \ = \ x+1+\frac{5}{x+2}?$

see graph below:

[attachment=0:n568zmeq]xxx.jpg[/attachment:n568zmeq]