need help with problem

Question

anonymous · Answer

post it

anonymous · Answer

err you need help but you want us to help or not?

anonymous · Answer

attachment

anonymous · Answer

my server was out for little bit, sorry!

anonymous · Answer

:D this site is really harms the machine -.-'

anonymous · Answer

that for sure, lol

anonymous · Answer

it looks like differential o.O

anonymous · Answer

yep!

anonymous · Answer

i cant bring up your diagram for some reason

anonymous · Answer

what version of windows do you have?

anonymous · Answer

ta just put your screen shot to paint and save it as .jpg file then there won't be any problem

anonymous · Answer

attachment

anonymous · Answer

attachment

anonymous · Answer

this is a lot easier than it looks at first glance, especially if you know how to take derivatives quickly.  do you?

anonymous · Answer

yes!

anonymous · Answer

good then the derivaitive from the left is -1 and the derivative from the right is 
$$\frac{1}{(7-x)^2}$$

anonymous · Answer

clear what i did right? for the left i used 
$$f(x)=7-x$$ and from the right i used 
$$f(x)=\frac{1}{7-x}$$

anonymous · Answer

to get the two derivatives.  then replace x by 6 
derivative from the left is a constant. it is -1
when you replace x by 6 in the second expression you get 1

anonymous · Answer

yes!

anonymous · Answer

it only looked hard

anonymous · Answer

ok, so does f' (6) exists, if does how would you find its values

anonymous · Answer

clearly not since 
$$1\neq -1$$

anonymous · Answer

oh ok, so  if they both had the same solution then, they would exists

anonymous · Answer

true?

anonymous · Answer

oh yes sorry. if the limits are the same then it exists and if not then no