导数五步法画函数图像10个函数示意图应用举例之一
\n\n
\n\n
1.函数y=(12x2+9)(4x2+14)的图像示意图：介绍函数的定义域、单调性、凸凹性、极限等性质及五点图表，并通过导数知识计算函数的单调和凸凹区间，简要画出示意图。
\n\n
2.函数y=(19x2+5)√(4x2+9)的主要性质及其图像：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，进一步画出函数的示意图。
\n\n
3.函数y=4√(x+80)^7图像画法及步骤：本文通过函数的定义、单调、凸凹性和极限等性质，介绍函数的主要性质及图像画法步骤。
\n\n
4.曲线x³+y³=2的主要性质及其图像示意图：介绍曲线方程的定义域、单调性、凸凹性等性质，同时用导数的知识求解函数的单调区间和凸凹区间，并简洁画出函数的图像示意图。
\n\n
5.√(x+4)+√(3y+5)=2的图像示意图：介绍曲线方程的定义域、单调性、凸凹性及极限等性质，同时用导数简洁画出函数的图像示意图。
\n\n
6.函数y=16x3+8x的图像示意图及主要性质：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，进一步画出函数的示意图。
\n\n
7.函数y=√(20x-87)^5图像画法及步骤：通过函数的定义、单调、凸凹和极限等性质， 并通过导数知识，介绍函数的主要性质及图像示意图画法步骤。
\n\n
8.函数y=log2(-2x+3)的图像示意图：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，简要画出函数的示意图。
\n\n
9.函数y=e^x(3x+4)的图像示意图：本文通过函数的定义、单调、凸凹性和极限等性质，介绍函数的主要性质及图像画法步骤。
\n\n
10.函数y=2^4x的图像示意图：介绍函数的定义域、单调性、凸凹性、极限等性质，列举函数的五点图表，进一步画出函数的示意图。
\n\n
\n\n
","gnid":"9758824ec7671aa4d","img_data":[{"flag":2,"img":[{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t01a370aba0dc0184ae.jpg","width":1280},{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t01fe729509bf6963a8.jpg","width":1280},{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t01c644eeab94a0efe6.jpg","width":1280},{"desc":"","height":925,"title":"","url":"https://p0.ssl.img.360kuai.com/t013539215e0a83c2a4.jpg","width":1280},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t011ac510957e2c014e.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01b6300bde0321b12c.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t010ec62f9edc968eba.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t012ea8cadd7067c59a.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0135e6b9e5ad5f2723.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0101a95b931e2c6661.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0156869fd05f1b9bb9.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01eeb16f6ae9877b62.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01fd234f62dc83b806.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01a7177f0c14cf1b67.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01f3e9bcbfa66207be.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0111341fafd83e8b23.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01b12ae4529c0fc1a5.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01c2d414e70ce33022.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01a6435466e13d89c7.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0179a153481db89522.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t013f7979ab67311565.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t012871721b42a710c1.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t013b8fb94c7da143c9.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t015c6380a9e4dd5da4.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01c8edbb39b9d7fe87.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0122b1ab788e519a35.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01b446dfdddb35e4bf.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01651411583c303362.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0126094f1ca9ed1956.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t018fabf5214cdfc785.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t015b3f1e97b4dbe1ae.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01190830f3a32242fd.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01f1055028c526dd9d.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01e3ef63beab75c785.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t011dde9de6ce8a849b.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t019e8dbf2156e3031f.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t017d660aed63d492fa.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t017d660aed63d492fa.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0173f2a15f98505230.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0121e883d03506ad7f.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01fd20ffaf7942432d.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0174518a47ce9dd664.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t013e8e7b19fa695693.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0130fe2d9574be5db9.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0143c4b32aae3b438c.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01f74b752f697884fa.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0117c554a911c21419.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t0141cfbe536892d640.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01d396d571728906e5.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t01c87a38b737bd03fb.jpg","width":"3509"},{"desc":"","height":"2481","title":"","url":"https://p0.ssl.img.360kuai.com/t018eaaf25c81dbece5.jpg","width":"3509"}]}],"original":0,"pat":"pdc,art_src_0,fts0,sts0","powerby":"pika","pub_time":1711495200000,"pure":"","rawurl":"http://zm.news.so.com/7339c860ffebb01ebf215d79eb02f630","redirect":0,"rptid":"65e62da3ddba0208","rss_ext":[],"s":"t","src":"仁新数学","tag":[],"title":"导数五步法画函数图像10个函数示意图应用举例之一
平融柱2406当b= - --时,一次函数y=x+b与y=2x+3的图像的交点在y轴左边 -
鱼颖侵18125719907 ______ 1 y=x+b ① y=2x+3 ② 联立①②得 x=b-3,y=2b-3 ∴交点(b-3,2b-3) 由题意得 b-3<0,解得b<3 b=______,随便填一个小于3的数 2 当x1<x2时,y1>y2,则y在定义域内,随x的增大而减小 ∴1-2m<0 ∴m>1/2 ∴m的取值范围是____m>1/2_____. 有问题请追问,谢谢.
平融柱2406与函数y=x^2+2x+3的图像关于原点对称的图像解析式是 -
鱼颖侵18125719907 ______[答案] 点(x,y)关于原点的对称点为(-x,-y) 所以只有把函数的y换-y,x换-x就行了 y=x^2+2x+3的图像关于原点对称的图像解析式 -y=(-x)^2+2*(-x)+3 y=-x^2+2x-3
平融柱2406把y=2x^2+x+3的图像按a=(3, - 1)平移到C',则C'的函数解析式?过程… -
鱼颖侵18125719907 ______ 新的点x′=x+3 y'=y-1 故x=x'-3,y=y'+1 原来的点满足原来的解析式,把x、y代入C就得到x',y'关系式,即为C' y'+1=2(x'-3)^2+(x'-3)+3 y'=2(x'-3)^2+x'-1
平融柱2406如图,二次函数y= - x2十2x+3的图象与x轴交于A、B两点,与y轴交于点C.顶点为D.(1)求函数图象的顶点D的坐标、对称轴以及与坐标轴的交点坐标;(2)自... -
鱼颖侵18125719907 ______[答案] (1)y=-x2十2x+3=-(x-1)2+4, 所以顶点D的坐标为(1,4),对称轴为直线x=1; 令y=0,则-x2+2x+3=0,解得x1=-1,x2=3, 所以A点坐标为(-1,0),B点坐标为(3,0); (2)当x<-1或x>3时,y<0; 因为a=-1<0, 所以x=1时,y有最大值4.
平融柱2406二次函数y= - x2+2x+3的图象开口向______,顶点坐标是______. -
鱼颖侵18125719907 ______[答案] ∵y=-x2+2x+3中的a=-1, ∴开口向下; ∵y=-x2+2x+3=-(x2-2x+1-1-3)=-(x-1)2+4 ∴顶点坐标为(1,4); 故答案为:下,(1,4)
平融柱2406在同一直角坐标系中一次函数Y=2X+3,Y=2X - 3的图像有什么位置关系 -
鱼颖侵18125719907 ______ 平行,垂直相距6,无交点.
平融柱2406一次函数y= - 2x+3的图像不经过的象限是 -
鱼颖侵18125719907 ______ 一次函数y=-2x+3的图像不经过的象限是第三象限.
平融柱2406画出函数y= - x2+2x+3的图象,并指出该函数的单调区间. -
鱼颖侵18125719907 ______[答案] 函数y=-x2+2x+3,x=1是函数的对称轴,函数的图象如下图所示: 由图象可得函数的单调递增区间为(-∞,1]; 函数的单调递减区间为[1.+∞).
平融柱2406做出y= - x^2+2x+3的图像,并求出函数的单调区间 -
鱼颖侵18125719907 ______[答案] y=-x^2+2x+3=-(x-1)^2+4 开口向下 单调增区间(-∝,1) 单调减区间(1,+∝)
平融柱2406函数y= - x²+2x+3的图像的顶点坐标是 -
鱼颖侵18125719907 ______[答案] y = -x² + 2x + 3 = -x² + 2x - 1 + 4 = -(x - 1)² + 4 所以顶点坐标 (1 ,4 )