已知函数f(x)=x3+ax2+bx+c在x=-23与x=1时都取得极值(1)求a,b的值和...
发布网友
发布时间：2024-10-24 11:17
共1个回答
热心网友
时间：18小时前
（1）∵f（x）=x3+ax2+bx+c，∴f′（x）=3x2+2ax+b，
∵函数f（x）在x=-23与x=1时都取得极值，
∴f′（-23）=0，f′（1）=0，
即f′（-23）=129-4a3+b=0，f′（1）=3+2a+b=0
得a=-12，b=-2，
经检验，a=，b=-2符合题意．
则f（x）=x3-12x2-2x+c，
∴f′（x）=3x2-x-2=（3x+2）（x-1），
列表
x（-∞，-23）-23（-23，1）1（1，+∞）f′（x）+0-0+f（x）↑极大值↓极小值↑，则函数的单调增区间为（-∞，-23）和（1，+∞）．
（2）由（1）可得函数f（x）的极大值为f（-23）=2227+c，极小值f（1）=-32+c，
要使y=b=-2与函数y=f（x）的图象有3个交点，
则2227+c＞-2-32+c＜-2，即c＞-7627c＜-12，即-已赞过已踩过你对这个回答的评价是？评论收起 ._1uevpeq{zoom:1;background-color:#fff;border:0;margin-bottom:10px;padding:30px 0 20px 42px;position:relative}._1uevpeq.ec-1841{padding:20px 0}._1uevpeq.ec-2246{padding:20px 0 10px}.ec-1841 .y7we4hu{font-size:16px;margin-bottom:-5px}.y7we4hu{color:#7a8f9a;height:25px;line-height:25px;overflow:hidden;position:relative}.y7we4hu h2{margin:0;padding:0}.y7we4hu:after{clear:both;content:" ";display:block;height:0;visibility:hidden}a.tycfu7u{color:#666;float:right;font-size:12px;margin-left:8px;text-decoration:none}.hhhv6ex{color:#666;font-size:13px;line-height:normal;line-height:20px;margin-top:10px}.vnsdjzp{margin-top:15px;position:relative}.vnsdjzp h3{font-weight:400;padding:0}.vnsdjzp a{text-decoration:none}.vnsdjzp em{color:#d81419;font-style:normal}.ec-2246 .vnsdjzp{margin-top:20px}._853bpkf{margin-top:10px}.a8gn2rz{margin-top:24px}._9rp2sus{display:block;overflow:hidden;width:auto}._4fuv54y,._85hk68c,.c84cjyj,.cd2v8yz,.gbuysgj,.gbxbqd2,.kpq54qk,.kw488k9,.puc33cm,.rdg9v5w,.yg47vz5{box-sizing:border-box;float:left;min-height:1px;position:relative}.cd2v8yz{width:8.33333333%}.gbuysgj{width:16.6666666%}.c84cjyj{width:25%}.puc33cm{width:33.33333333%}._85hk68c{width:50%}.rdg9v5w{width:58.3333333%}.kw488k9{width:66.66666667%}.kpq54qk{width:75%}.gbxbqd2{width:83.3333333%}._4fuv54y{width:91.66666667%}.yg47vz5{width:100%}.hc9wng2{float:right}body a.xny78f9,body div.xny78f9{color:#333;display:block;font-family:Arial,Helvetica,sans-serif;font-size:14px!important;line-height:19px;margin-bottom:10px;text-decoration:none}a.xny78f9:hover{color:#34b458;text-decoration:underline}a.xny78f9 font{color:#34b458}a.xny78f9 div{word-break:break-all}.v3zrcrj{overflow:hidden;text-overflow:ellipsis;white-space:nowrap}.q1dpns8{-webkit-line-clamp:2}.ndfxdqz,.q1dpns8{word-wrap:break-word;-webkit-box-orient:vertical;display:-webkit-box;overflow:hidden;word-break:break-all}.ndfxdqz{-webkit-line-clamp:3}._7qtpw9j{-webkit-line-clamp:4}._2dt35k2,._7qtpw9j{word-wrap:break-word;-webkit-box-orient:vertical;display:-webkit-box;overflow:hidden;word-break:break-all}._2dt35k2{-webkit-line-clamp:5}._1r3uysh{-webkit-line-clamp:10}._1r3uysh,.yux2cc6{word-wrap:break-word;-webkit-box-orient:vertical;display:-webkit-box;overflow:hidden;word-break:break-all}.yux2cc6{-webkit-line-clamp:12}._4bxpxs9{-webkit-line-clamp:18;word-wrap:break-word;-webkit-box-orient:vertical;display:-webkit-box;overflow:hidden;word-break:break-all}body .k795fxy{color:#7a8f9a;font-family:Arial,Helvetica,sans-serif;font-size:12px;line-height:22px;padding-top:0;position:relative;transform:translateY(.4666666667em)}body .k795fxy:before{content:"";display:block;height:0;margin-top:-10px}body .k795fxy a{color:#7a8f9a;display:block}body .k795fxy a ._1nczxan{color:#666}body .k795fxy button{background:#fff;border:1px solid;border-radius:3px;bottom:0;color:#38f;float:right;font-size:12px;line-height:12px;padding:7px 13px;position:absolute;right:0}body .k795fxy .db1j6uz{margin-left:5px}body .k795fxy .mxyzxgv{border:1px solid #eee;border-radius:50%;display:inline-block;height:22px;line-height:0;margin-right:7px;margin-top:-2px;vertical-align:middle;width:22px}body .k795fxy .accwaqu{margin-right:8px}.zdjeshn{position:absolute;right:0}.tx6hcqf{-webkit-box-orient:horizontal;-webkit-box-align:stretch;-webkit-align-content:flex-start;-webkit-align-items:stretch;display:-webkit-flex;-webkit-flex-wrap:nowrap;-webkit-justify-content:space-between;width:auto}.bde3hfs{flex:1}body .k795fxy a.n1yex5p,body .k795fxy div.n1yex5p{display:flex;justify-content:space-between}.k795fxy .ec-showurl-line:hover{text-decoration:underline}.k795fxy .ec-showurl-line{color:#9eacb6}.k795fxy{padding-bottom:1px}@charset "UTF-8";body ._886bxmw{font-size:12px;line-height:22px;padding-top:0;transform:translateY(.4166666667em)}body ._886bxmw:before{content:"";display:block;height:0;margin-top:-10px}body ._886bxmw a,body ._886bxmw div{color:#333}body ._886bxmw .d81nas8{color:#999;font-size:15px;line-height:25px}body ._886bxmw ._9mnfgfc{margin-right:5px}._886bxmw font{color:#34b458}.ec-2246 ._886bxmw font{color:#c60a00}.ec-2246 ._886bxmw{font-size:16px}.ec-2246 ._8gpc1uj{position:relative}.ec-2246 ._8gpc1uj:after{background-color:#fff;bottom:0;color:#34b458;content:"点击查看详情";display:inline-block;padding-left:10px;padding-right:0;position:absolute;right:0}.ec-2246 ._8gpc1uj:before{background-image:linear-gradient(270deg,#fff,hsla(0,0%,100%,0));bottom:0;content:"";height:29px;position:absolute;right:90px;width:47px}.qeb9494{padding-bottom:100%}.cbnvsmc{padding-bottom:133.33333333%}.bd8dsh2{padding-bottom:33.3333333333%}.s8vwdyg{padding-bottom:56.25%}._77yj6{padding-bottom:50%}._3hu75mr{padding-bottom:75%}.kdcm6p9{padding-bottom:66.66666667%}.xgdthff{padding-bottom:40%}.wagcupv{background-position:50%;background-repeat:no-repeat;background-size:cover}._3hu75mr,._77yj6,.bd8dsh2,.cbnvsmc,.kdcm6p9,.qeb9494,.s8vwdyg,.xgdthff{height:0;overflow:hidden}._3hu75mr img,._77yj6 img,.bd8dsh2 img,.cbnvsmc img,.kdcm6p9 img,.qeb9494 img,.s8vwdyg img,.xgdthff img{width:100%}.dycvwv4{border-radius:9px}._1kcc4s3{border-top-left-radius:0}.f9mstuk{border-top-right-radius:0}._24395ct{border-bottom-right-radius:0}.r1yfcd1{border-bottom-left-radius:0}.qd9k1mu{color:#333;font-size:14px;line-height:24px;margin-top:2px}.qhn3ktc{color:#f60;font-size:14px;line-height:22px;margin:5px 0;vertical-align:middle}._6ad8bqy{position:relative}.a85j8fv{background:radial-gradient(transparent 50%,rgba(0,0,0,.05) 100%);height:100%;left:0;position:absolute;top:0;transform:translateZ(0);width:100%}.dycvwv4 .a85j8fv{border-radius:9px}._1kcc4s3 .a85j8fv{border-top-left-radius:0}.f9mstuk .a85j8fv{border-top-right-radius:0}._24395ct .a85j8fv{border-bottom-right-radius:0}.r1yfcd1 .a85j8fv{border-bottom-left-radius:0}._6ad8bqy.qeb9494{height:92px;padding-bottom:0}.ec-2246 ._6ad8bqy.kdcm6p9{height:160px;margin:auto;padding:0;width:240px}body .c69sfzc{display:flex;font-size:0;overflow:hidden}body ._5dn6uyv{margin-right:8px;max-width:35px;min-width:35px;vertical-align:top}body .qrpnxfs{background:url(//nv00.cdn.bcebos.com/nv01/static/ecom/img/pc/head-img-535c333798.png) no-repeat 50%;background-size:100% 100%;height:100%;width:100%}body .nmkjhaf{height:35px;min-width:0}body .v1ftvns{color:#000;font-size:16px;font-weight:inherit;line-height:1;margin-bottom:8px;overflow:hidden;text-overflow:ellipsis;white-space:nowrap}body ._7pt3pe5{color:#999;font-size:12px;line-height:1}body .c69sfzc .m11ehk9 img{width:100%}body .c69sfzc ._7enmqsz{margin-right:15px}body ._5dn6uyv{border-radius:50%;max-width:40px;min-width:40px;overflow:hidden}body .v1ftvns{color:#333;font-size:14px;font-weight:700;line-height:20px;margin-bottom:0}body ._7pt3pe5{color:#9eacb6;line-height:17px;margin-top:3px} 百度教育广告2024-11-18初二数学函数知识点完整版下载，海量试题试卷，全科目覆盖，随下随用，简单方便，即刻下载，试卷解析，强化学习，尽在百度教育www.baidu.com !function(t){"use strict";function e(t,e){if(t){var n=new Date().getTime(),i=new Image;t+="&rand="+(n+Math.random()),window.ecomLogImage||(window.ecomLogImage={}),window.ecomLogImage["--IMAGE"+n]=i,e=e||{};var r=!1;i.onload=i.onerror=i.onabort=function(o){if(!e.charge){if(o&&"load"!==o.type){if(r)"error"in e&&e.error();else{i.src=t,r=!0;return}}else"load"in e&&e.load()}i.onload=i.onerror=i.onabort=null,window.ecomLogImage["--IMAGE"+n]=null,i=null},i.src=t}}var n,i=function(){var t,e,n,i=0,r=0,o=0,s=0,a=0,c=0,u=0,l=0,h=/link\?url\=([^\&]+)/,f=/\?url\=([^\.]+)\./,d="data-cklink",p=/[?&]tn=([^&]*)/;function v(t){if(!t)return!1;var e=h.exec(t)||f.exec(t);return!!e&&(h.exec(t)?e[1].length
