Question

How do you find zeros of functions involving exponentials?

Answer 1

I need help on #13 and 14 please

Answer 2

You can factor number 13
notice both terms have a common factor of e^x

Answer 3

You can also factor number 14

Answer 4

also e^(whatever) will never be zero

Answer 5

oh ok didnt see that

Answer 6

that makes sense

Answer 7

so wud 13 be x+1 factored?

Answer 8

well your f(x)=e^x (x+1)
and we said e^x is never 0
so you just find when x+1 is 0

Answer 9

\[e^x (x+1) =0 \\ e^{x} \neq 0 \text{ so you just solve } x+1=0\]

Answer 10

x= -1 then?

Answer 11

Yep number 13 only has the one zero which is x=-1

Answer 12

number 14 is very similar
except you should have two zeros

Answer 13

nice :D

Answer 14

ok ill try it now

Answer 15

so you would factor out e^-x right?

Answer 16

yes

Answer 17

and e^(whatever) never zero

Answer 18

questions 13-16
all of these you can write as e^(some variable) * (polynomial)
and the zeros will always come from solving polynomial=0
since e^(some variable) is never 0

Answer 19

ok so the next step would be just solving -x^2+2x=0?

Answer 20

that's right

Answer 21

would you factor out -1 first

Answer 22

how about -x?

Answer 23

ah ok lol

Answer 24

well then what happens to the -x^2? does it juts turn to 1?

Answer 25

no

Answer 26

-x*x=-x^2
-x*-2=2x

so -x^2+2x can be written as -x(x-2)

Answer 27

ah ok that makes sense

Answer 28

so the zeros are 0 and 2?

Answer 29

yes perfect

Answer 30

ok thank you so much :D