题目

One wet, rainy April afternoon Miss O’ Shay, the principal, sent for Nancy Lee to stop by her office as school closed. Pupils without umbrellas or raincoats crowded in doorways hoping to make it home between showers. Outside the skies were grey. Nancy Lee’s thoughts were suddenly grey, too. She did not think she had done anything wrong, yet that tight (紧的 ) little knot came in her throat just the same as she came near Miss O’Shay’s door. Perhaps she had banged her locker too often and too hard. Perhaps the note in French she had written to Sallie halfway across the study hall just 已知函数，过点P（1，0）作曲线y=f（x）的两条切线PM，PN，切点分别为M，N．（1）当t=2时，求函数f（x）的单调递增区间；（2）设|MN|=g（t），试求函数g（t）的表达式；（3）在（2）的条件下，若对任意的正整数n，在区间内，总存在m+1个数a1，a2，…，am，am+1，使得不等式g（a1）+g（a2）+…+g（am）＜g（am+1）成立，求m的最大值．