题目

（21）已知a＞0，函数f（x）=x3－a，x∈［0，+∞).设x1＞0，记曲线y=f（x）在点M（x1，f（x1））处的切线为l.（Ⅰ）求l 的方程；（Ⅱ）设l与x轴交点为（x2，0）.证明： 答案：（21）本小题主要考查利用导数求曲线切线的方法，考查不等式的基本性质，以及分析和解决问题的能力.（Ⅰ）解：求f（x）的导数：f′（x）=3x2，由此得切线l的方程：y－（x－a）=3x（x－x1）（Ⅱ）证：依题意，切线方程中令y=0， x2=x1－=， 阅读理解。You can't play, walk, skate or ride a bike on the railroad(铁路). There are many places where the railroad tracks cross roads or streets. Many of these railroad crossings are marked(标注) with one of the signs in the table(表) below.1. This sign means you are coming to a railroad crossing. Always look both sides and listen carefully to be sure a train is not coming from either direction before crossing the tracks.2. Many railroad crossings have a gate with flashing lights that close when a train is coming.● NEVER go around a closed railroad gate.● NEVER try to get across the tracks before the train gets there.3.Some crossings which don't have gates may have this sign. When the lights are flashing, a train is coming. You should wait until the train has passed before trying to cross the tracks.Be careful when crossing railroad tracks:● Railroad tracks are uneven(凹凸不平的). You should not bicycle, skate or run when crossing tracks.● Trains are very large and heavy, and take a long time to stop.● Sometimes when a train has just passed from one direction, another train may be coming from the opposite direction. You might not notice the second train because of the noise from the first train.1.The underlined word "tracks" means in Chinese.A．轨道 B．足迹C．标志 D．小路2.When you see Sign One, you should .A．not pass the railroad crossingB．stop to wait for a car to passC．make sure no train is coming before you crossD．pass the railroad crossing immediately3.Where can you see Sign Three on the railroad?A．On the railroad tracks.B．At the train stations.C．At crossings that have gates.D．At crossings that have no gates.4.What can we learn from the passage?A．We can see many railroad signs in our cities.B．There are many gates on the railway tracks.C．It takes a short time for a train to stop.D．It's dangerous to play, run or bicycle on the railroad.5.What's the best title for the passage?A．How to Cross the Railroad Tracks SafelyB．Pay Attention to Some Train SignsC．Don't Play on the Railroad TracksD．How to Protect the Railroad Tracks