【題目】某人上午
時(shí)， 乘摩托艇以勻速
從
港出發(fā)到距
的
港去， 然后乘汽車以勻速
自港向距
的
市駛?cè)ィ畱?yīng)該在同一天下午
至
點(diǎn)到達(dá)市． 設(shè)乘坐汽車、 摩托艇去目的地所需要的時(shí)間分別是
.
（1）作圖表示滿足上述條件的
范圍；
（2）如果已知所需的經(jīng)費(fèi)
（元），那么
分別是多少時(shí)
最小？ 此時(shí)需花費(fèi)多少元？
【答案】（1）
；（2）
的最小值為
元．
【解析】
試題分析：（1）依題意得 
解出
所滿足的范圍，作出符合條件的圖形；（2）先確定目標(biāo)函數(shù)，由題意得得出
，由（1）中圖可知，當(dāng)先經(jīng)過(guò)點(diǎn)
時(shí)，目標(biāo)函數(shù)取得最小值，即可求解結(jié)論.
試題解析：（1）依題意得
①
由于乘汽車、摩托艇所需的時(shí)間和
應(yīng)在
至 
個(gè)小時(shí)之間，即
②
因此，滿足①②的點(diǎn)
的存在范圍是圖中陰影部分（包括邊界）
（2）
，上式表示斜率為
的直線，
當(dāng)動(dòng)直線通過(guò)圖中的陰影部分區(qū)域（包括邊界），通過(guò)點(diǎn)
時(shí)，
值最小．
由
得
，即當(dāng)
時(shí)，
最小．
此時(shí)，的最小值為 
元．
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A
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