Question

f(x) = e^6x + e^−x
Find increasing and decreasing intervals. I understand how to do these questions, but I get really confused when they do it with the e

Answer 1

ok how u find increasing interval??

Answer 2

I need to find the derivative and then do a number line

Answer 3

u know the derivative of e^ something??

Answer 4

So far I got up to =6e^6x-e^-e

Answer 5

I dont know what to do after that

Answer 6

what u do to find increasing or decreasing interval in general ??

Answer 7

after finding derivative

Answer 8

I found the critical numbers and then made a number line and saw where it was increasing and decreasing

Answer 9

I set the first derivative = 0

Answer 10

\[6e^{6x}-e^{-x}=0\]

Answer 11

The function is increasing when its first derivative is ----
The function is decreasing when its first derivative is ----
know what comes in those blanks ?

Answer 12

add e^-x on both side

Answer 13

would I then get e^-x (6e^5x-1)=0 ?

Answer 14

hartnn said right first we need to assure it is greater than 0 or less than 0 after that we will find the interval by puttin it equal to zero

Answer 15

\[6e^{6x}-e^{-x}+e^{-x}=e^{-x}\]

Answer 16

what u will get ??

Answer 17

6e^6x=e^-x

Answer 18

yeah ...u know??
x^(-a)=1/x^a it can also written like this also

Answer 19

@sheetalvee

Answer 20

oh okay, I didnt know that

Answer 21

okay leave ...it ..take natural log on both side

Answer 22

okay. so 6x log 6e = -x log 6 ?

Answer 23

\[\log_e (6*e^6x)=\log_e e^{-x}\]

Answer 24

log 6+ 6x*log e= -x log e

Answer 25

when number and base are equal the its value =1
like here base= e and number =e

Answer 26

log6+6x*1=-x*1
tell me what u got

Answer 27

log6=-7x ?

Answer 28

log_e 6=1.79

Answer 29

1.79=-7x

Answer 30

divide both side by 7

Answer 31

i prefer to take inequalities from beginning only

increasing when
\(6 e^{6x} > e^{-x} \)

decreasing when
\(6 e^{6x} < e^{-x} \)

Answer 32

yes thatz is the best way..i carried bcoz she said she put =0

Answer 33

wait how did you get 1.79

Answer 34

u got the crictical point now

Answer 35

we took natural log
so natural log of 6 = 1.79

Answer 36

also by now
you should be able to solve it like this :

without using logs
if you can't, then better learn it now :)