Question

PLEASE HELP if gPRIME(x)=2g(x) and g(-1)=1. then g(x)=
1) e^(2x)
2) e^(-x)
3)e^(x+1)
4) e^(2x+2)
5) e^(2x-2)
explanation would be greatly appreciated

Answer 1

:) i think checking the options out is the easiest way
we know that g(-1)=1
so you check the options
put x=-1 in them
the the expression which equals 1 is answer
When we check option 3 and option 4 are suitable answer

But there will only be 1 solution
So now we see that whos gPRIME(x) will equal 2g(x)
can you do from here? :)

Answer 2

i dont think so, i'm sorry can you assist me

Answer 3

ok :)
is it clear that the solution is either 3 or 4?

Answer 4

Yes i understand that, when we plug in -1 into the x the answer is 1 for both

Answer 5

and we already have an example which shows that g(-1)=1

Answer 6

i'm confused what we plug into the derivatives of options three and four to know which one is the answer

Answer 7

ok 1st lets find out the derivative of option 3

Answer 8

2e^(2x+2)

Answer 9

^this is the derivative or gPRIME(x) of the option number 4 :D

Answer 10

oh shoot I apologize I did the wrong one first

Answer 11

e^(x+1)

Answer 12

llol its ok
so it is gPRIME(x) of the 4th option g(x)=e^(2x+2)

can you find a relation between
gPRIME(x) and g(x) :)

Answer 13

yes thats also correct
e^(x+1) is correct derivative for 3rd option :)

Answer 14

its mulitplyed by 2....?

Answer 15

yes :D
and now read the ques and check if option 4 satisfy all those conditions :)

Answer 16

OH MY GOODNESS that's too cool

Answer 17

yeah B)

Answer 18

thank you very much :)

Answer 19

No problem (B