Question

PLEASEEE HELP! determine:
a) increasing/decreasing intervals
b) concavity intervals
c) extrema
d) inflection points
of the attached function.

Answer 1

\[f(x) = e ^{x-1} - x\]

Answer 2

\[f('x) = e ^{x-1}-1\]

Answer 3

@zepdrix

Answer 4

Ughhh these problems are so annoying XD You're still doing these?? lol

Answer 5

unfortunately ): they suck. do you know how? i need potato math.

Answer 6

lolololol

Answer 7

Ummm so your first derivative looks good.
Setting it equal to 0 to find critical points, hmm what do we find out? :D

Answer 8

i got x =1... haha. is that right?

Answer 9

\[\large 0=e^{x-1}-1\]\[\large 1=e^{x-1}\]
Hmmm yesss sounds right! :D

Answer 10

okay. well now im confused on how to find intervals ):

Answer 11

Ummm, well in your class, how have you been doing it?
Which method?

Making a chart?
or
Drawing a number line with arrows?

Answer 12

Cause I'd rather do it the way you're familiar with :3 heh

Answer 13

number line pretty much. but doesnt there have to be a sign change? there isnt a sign change when i plug in a number greater than and less than 1..

Answer 14

Hmmm there should be a sign change! :) Because of the minus 1 part.

If you plug in a value x<1
Your exponential will be e^(negative number) , which is slightly less than 1.
So you'll end up with a negative sign.

If you plug in a value x>1
Your exponential will be a little bit bigger than e^0, which is slightly larger than 1.
So you'll end up with a positive sign!

If you're confused I can give an example :D

Answer 15

oh.. idk when i plug it into the calc it always gives me a positive. wow maybe im doing it wrong. i stinkkk.

Answer 16

\[\large f'(1.1)=e^{0.1}-1= \; 1.105-1=\;+\]

Answer 17

Oh calculator trouble? :O dang

Answer 18

Make sure you're plugging the values into the derivative function :D

Answer 19

\[\large f'(0.9)=(e^{-0.1})-1=(0.904)-1= \; (-)\]

Answer 20

okay sooo would my decreasing interval be (-∞, 1]
and increasing interval is [1, ∞) ?

Answer 21

Mmmmmm yahhhhh that sounds right I think :D

Answer 22

Yah, yah yah

Answer 23

What does that tell you about x=1? :D Min? max? Potato??

Answer 24

POTATO. no. that would tell me that x=1 is a min.

Answer 25

wait so is that an answer for my extrema?