Question

Demonstrate:

Answer 1

Demonstrate what?

Answer 2

\[e ^{x}\ge x+1\]

Answer 3

Hmm, well the power series representation of e^x is \[e^x= 1+x+\frac{x^2}{2}+\frac{x^3}{3!}+\frac{x^4}{4!}+...\]

or you could just plug in a number to show that I guess. How exactly do you want to demonstrate it?

Answer 4

This problem represents an application to derivative functions so..

Answer 5

If you show that they're the same at x=0 then take the derivative of both you can compare their slopes. Since e^x has a much steeper slope than x+1 we know that it must be greater because it is increasing faster and the other function can't catch up to it.