I've had two answers to my
question on Spivak's proof of theorem 1 in the appendix of chapter 8 of Calculus, yet I can not understand why $f$ is $\epsilon$-good on $[\alpha-\delta_0,\alpha+\delta_0]$. For all $y,z\in[\alpha-\delta_0,\alpha+\delta_0]$, we have $|y-\alpha|\le\delta_0$ and $|z-\alpha|\le\delta_0$. What do these two inequalities imply?