If f'(x) = f(x) for all x what is g'(x)?Hello. I am confused by this problem question … I can’t figure out how to determine f from the information given. I will post my work this far… can anyone help please? ?View attachment 33170View attachment 33171
TIf f'(x) = f(x) for all x what is g'(x)?
-Dan
Thanks for the help so far.. I have tried to find g’(x) but just can’t figure out how that could allow me to determine f as asked in question 6(b). this is my work this far.Your work is incomplete!
You have that 1*f(0) = a. So solve for f(0).
You really need to use your knowledge of the 1 times table!
You have \(\displaystyle g'(x) = e^{-1}f'(x) + (-e^{-1})f(x).\) Now clean this up! Then use the fact that f'(x)=f(x)
A prerequisite for Calculus 1 is Algebra
In your work, third line from the end, you write:T
Thanks for the help so far.. I have tried to find g’(x) but just can’t figure out how that could allow me to determine f as asked in question 6(b). this is my work this far.
If I asked you what 3 - 3 is, what would you tell me? So what is f(x) - f(x)?T
Thanks for the help so far.. I have tried to find g’(x) but just can’t figure out how that could allow me to determine f as asked in question 6(b). this is my work this far.
I see my mistake here. So g’(x) = e^-x (0) which equals 0 … so g’(x)=0. But I just don’t understand how this derivative can help me to find f. I know if g’(x) = 0 then g(x) = e^-x*f(x) must be a constant …. But I can’t figure out how to find f.
g(x) = e^-x*f(x) = KIf I asked you what 3 - 3 is, what would you tell me? So what is f(x) - f(x)?
I see my mistake here. So g’(x) = e^-x (0) which equals 0 … so g’(x)=0. But I just don’t understand how this derivative can help me to find f. I know if g’(x) = 0 then g(x) = e^-x*f(x) must be a constant …. But I can’t figure out how to find f.
Yes . I understand g(x) is K … a constant. So g(x) = e^-x*f(x) is a constant .. I still don’t know how to find f. I’m sorry I know I must obviously be missing something obvious but I just can’t get itDid you read response #6 ?
Work with pencil/paper - don't just stare at the screenYes . I understand g(x) is K … a constant. So g(x) = e^-x*f(x) is a constant .. I still don’t know how to find f. I’m sorry I know I must obviously be missing something obvious but I just can’t get it
Yes ..... you got it....f(x) = Ke^x ???