Prove an inequality -- my problem

[lookagain]

Let $\displaystyle m$ belong to the set of real numbers. Prove for $\displaystyle \ \ m \le -0.75:$ Edit:


0.8 is the wrong constant.


$\displaystyle 2^m < m^2$

 

[Denis]

Re: Prove an inequality

Let $\displaystyle m$ belong to the set of real numbers. Prove for $\displaystyle \ \ m \le -0.8:$
$\displaystyle 2^m < m^2$

Hmmm....try m = 2

 

[lookagain]

Edit: The wrong constant was used.

 

[Bob Brown MSEE]

decreasing vrs increasing

Let $\displaystyle m$ belong to the set of real numbers. Prove for $\displaystyle \ \ m \le -0.8:$

$\displaystyle 2^m < m^2$

f=2^m, f'=(ln2)f -> increasing on m<-0.8
g=mm, g'=2m -> decreasing on m<-0.8
f=g at m=-0.77

 

[lookagain]

f=2^m, f'=(ln2)f -> increasing on m<-0.8



g=mm, What!? $\displaystyle g = m^2$

g'=3m ->What!? g' = 2m

decreasing on m<-0.8



f=g at m=-0.77 . . . No, $\displaystyle m \approx -0.77$

$\displaystyle At \ \ m \ = -0.77, \ \ 2^m \ < \ m^2.$

 

[Bob Brown MSEE]

Applied Math

$\displaystyle At \ \ m \ = -0.77, \ \ 2^m \ < \ m^2.$

-0.77 means approximately -0.77
-0.7700000... (repeated decimal) has the meaning that you inferred.
Since it does not matter (to my point) where in the interval (-0.775, -0.765) that equality occurs,
I used the (correct) interpretation that a non-repeating decimal is not exact.

The typo 3m should have been 2m (as you correctly pointed out) -- thanks -- I edited it.

The fact that you do not understand what mm means, requires no comment.

 

[Bob Brown MSEE]

Sorry Lookagain

Make the changes, don't make excuses, and move on.

** If you hadn't typed mm for m squared to begin with, I would anticipate that you would
have calculated the derivative correctly. As it is, as long as you continue to type it that way,
you're needlessly inviting error in judgment.

My intent was to clarify the difference between an exact expression and one that is approximate.

Important:
1) I agree that I made an error 3m should be 2m,
2) I edited all of the errors.
3) Thankyou for catching that error!!!!!!!!!