please check answer!!! picture included I got the answer C) f is discontinuous

Question

anonymous · Answer

attachment

zepdrix · Answer

Discontinuity at x=1 ? Hmm...$$\large\rm f(x)=\ln x+e^{-x}$$$$\large\rm f(1)=\ln 1+e^{-1}$$$$\large\rm f(1)\approx 0.368$$

zepdrix · Answer

So derivative and stuff, ya?
Find critical points? :)

anonymous · Answer

i tryed to find the critical points

anonymous · Answer

i only got x=0

zepdrix · Answer

You got x=0 for a critical point?
Hmm I'm not able to find any critical points.

zepdrix · Answer

I think what we need to do is take a derivative,
then simply plug in x=1 and see what's going on.

If the result is `positive`, then the function is `increasing`
If the result is `negative`, then the function is `decreasing`.

zepdrix · Answer

If the result is `zero`, then yes we have some type of extrema :)

anonymous · Answer

the dericative i got was 1/x-(e^-x)

zepdrix · Answer

Looks good :)
What do we get when we plug in x=1?

anonymous · Answer

rounded to the third number it is .632

zepdrix · Answer

Good good good,
so which option? :D

anonymous · Answer

the function is increasing!

zepdrix · Answer

Yay team \c:/

anonymous · Answer

thank you very much for your assistance

zepdrix · Answer

np