differentiable function; derivate

A P-Function is a Differentiable function f: R→R with a continuos derivative f' on R such that f(x+f'(x)) = f(x) for alll x in R.

Prove that a P-function whose derivative has as least two distinct zeros is constant

I really need a help!

Easy Math Editor

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Comments

Okay, so here is what I see. If f(x+f'(x))=f(x), then x+f'(x)=x Then if you solve f'(x) by itself, then we get: f'(x)=0 If f'(x)=0, then that means every point on the graph will follow the line y=0, every value in the derivative is 0. Now recall, if f(x)=c, then f'(x) will be equal to 0. Therefore: when f'(x)=0, f(x)=c I hope this gets you to the solution you needed. I had to think about this one for a minute too. This may not be the formal way of doing the proof, but this will certainly be enough for you to be able to do it.

Dacota Sprague - 1 year, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$