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Can we construct a function $f(x)$ such that for every $x$

$f(x) =c$

and

$f'(x)=c$

What would be an example of such a function?

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closed as off-topic by Saad, Brahadeesh, Cesareo, ancientmathematician, Claude Leibovici Sep 27 '18 at 11:52

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  • $\begingroup$ For all $x$?... $\endgroup$ – Randall Sep 27 '18 at 1:23
  • $\begingroup$ The derivative of a constant function is identically zero. $\endgroup$ – dxiv Sep 27 '18 at 1:24
  • $\begingroup$ Well no: the derivative of a constant is $2 \neq 0$. $\endgroup$ – Randall Sep 27 '18 at 1:24
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If a function is identical to a constant, then it's derivative is $0$. So the only such function would be $f(x)=0 $ since $f'(x)=0$ also.

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Derivative of a constant is obviously zero..So if f(x)= a constant, only f(x)=0 can be applicable for the question you asked.

But if you want any variable functional value then "Exponential Function e^x" is always ready for you.

i.e f(x)= e^x

and f '(x)=e^x

Rather upto the nth derivative you'll get e^x ( n being a natural no )

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