Logarithmic func. determine the local exterma...

[wind]

Determine the local extrema, inflection points, and all asymptotes of reach function.

\(\displaystyle \L\ y= x - e^{x}\)


local extrema

\(\displaystyle \L\ y'= 1- e^{x}\)

\(\displaystyle \L\ 0= 1- e^{x}\)

\(\displaystyle \L\ -1=- e^{x}\)

\(\displaystyle \L\ ln(-1)=ln(-e^{x})\)

\(\displaystyle \L\ ln(-1)=xln(-e)\)

\(\displaystyle \L\frac{ln(-1)}{ln(e)}=x\)

\(\displaystyle \L\frac{ln(-1)}{1}=x\)

\(\displaystyle \L\ 3.14159265=x\) ( does that equal pi?)

inflection points
set up a chart

asymptotes

vetical=no
horizontal= ...how do i do this?
oblique= no

 

[skeeter]

\(\displaystyle y' = 1 - e^x\)

\(\displaystyle 1 - e^x = 0\)

\(\displaystyle 1 = e^x\)

\(\displaystyle x = 0\) because \(\displaystyle e^0 = 1\), right?

\(\displaystyle y'' = -e^x\) ... y'' < 0 for all x ... y is concave down, so there exists an absolute max at x = 0. The absolute max is y = -1

now ... graph the function in your calculator and confirm.

btw ... there are no asymptotes of any sort.

do you also know that you cannot take the log of a negative value?