- #1

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## Homework Statement

Assuming that (e

^{x})’ = (e

^{x}) at all point x, prove that e

^{c }= sinh(1) for some point C [tex]\in[/tex] (-1,1). Give the full proof.

## Homework Equations

## The Attempt at a Solution

I honestly dont know how to attempt this. i can show that (e

^{x})’ = (e

^{x}) by:

(e

^{x}) = 1 + x + x

^{2}[tex]/2![/tex] + x

^{3}[tex]/3![/tex] + x

^{4!}+ x

^{5}[tex]/5![/tex] +...

(e

^{x})’ = 1 + x + x

^{2}[tex]/2![/tex] + x

^{3}[tex]/3![/tex] + x

^{4!}+ x

^{5}[tex]/5![/tex] +...

I just dont know how to tackle the sinh part of the equation.

I would really appreciate any help/ guidance