Left continuous random walk argument

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In the preceding example given, I am unclear

1) why $\alpha<1$ results in $\phi \left(\alpha \right)=1$ The only value on an exponential that results in 1 is 0.

The only value such that makes this true is a zero value on an exponent.

2) $\phi\left ( 0 \right )=1$ and $\phi'\left ( 0 \right )>0$

What? The derivative of a constant is positive?

This is frustrating. I would appreciate if anyone could clarify the above.

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