If f'(x)=-f(x) and f(1)=1, find f(x).

Answer: e^(1-x)

Please show all the work.

If f'(x)=-f(x) and f(1)=1, find f(x).

Answer: e^(1-x)

Please show all the work.

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Fairport, NY

df/dx=-f, df/f=-dx, integrating both sides ln(f)=-x +c, at x=1 f(1)=1 so c=1, ln(f)=-x+1, and f(x)=e^{(1-x)}

Jim

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