perplexus.info :: Calculus : Finding the Function

Finding the Function (Posted on 2023-12-30)

Determine f(x), given that:
f'(x) = f(x+1)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Solutions?

Comment 1 of 1

The trivial f(x)=0 works.

f(x)=e^(x-floor(x)) also works except f' is undefined at the integers.

You can replace floor(x) with ceil(x) or with round(x). The latter shifts the f' problem to the half-integers.

This only works because with f(x)=e^x we have f'(x)=f(x).

https://www.desmos.com/calculator/5iat6elen1

Posted by Jer on 2023-12-30 10:54:24

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