perplexus.info :: Calculus : Back to derivative basics

Back to derivative basics (Posted on 2024-01-22)

Find all functions f:R⁺->R satisfying:

f(1)=1,
f has second derivative and
f'(1/x)=-(1/2)f(x).

No Solution Yet Submitted by Danish Ahmed Khan

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a thought...

| Comment 1 of 2

This works except for a sign change:

f(x) = c x^(1/2)

f'(x) = (c/2) x^(-1/2)

f'(1/x) = (c/2) x^(-1/2) = (1/2) f(x), but not -(1/2) f(x)

Edited on January 23, 2024, 8:58 am

Posted by Steven Lord on 2024-01-23 05:32:44

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