x∈(a,b)时(x-a)(x-b)≤[(b-a)/2]^2 若函数f（x）=x^2+(a+2)x+3，x∈[a,b]的图...
\u5df2\u77e5f(x)\u5728\u95ed\u533a\u95f4[a,b]\u5185\u4e25\u683c\u5355\u589e\uff0c\u800c\u4e14\u662f\u4e0b\u51f8\u51fd\u6570\uff0c\u8bc1\u660e\uff1a\u222b(a,b)f(x)dx\u22641/2(b-a)[f(a)+f(b)]\u51e0\u4f55\u610f\u4e49\u4e0a\u8bf4,\u66f2\u7ebff(x)\u4e0e\u76f4\u7ebfx=a,x=b,x\u8f74\u56f4\u6210\u7684\u66f2\u8fb9\u68af\u5f62\u7684\u9762\u79ef,\u8981\u5c0f\u65bc\u9876\u70b9\u4e3a(a,0),(b,0),(a,f(a)),(b,f(b))\u7684\u76f4\u89d2\u68af\u5f62\u7684\u9762\u79ef.\u8fd9\u4e2a\u81ea\u5df1\u7ed3\u5408\u56fe\u50cf\u5c31\u80fd\u5f88\u6e05\u695a\u770b\u51fa\u6765\u6211\u5c31\u4e0d\u591a\u8bf4\u4e86.
\u4e25\u683c\u8bc1\u660e\u7684\u8bdd\u4e5f\u5f88\u7b80\u5355.\u7531\u4e0b\u51f8\u51fd\u6570\u7684\u5b9a\u4e49,\u5728\u533a\u95f4[a,b]\u4e0a,\u5bf9\u65bc\u4efb\u610f\u03bb\u2208(0,1),\u90fd\u6709f[\u03bba+(1-\u03bb)b]\u2264\u03bbf(a)+(1-\u03bb)f(b)
\u4ee4x=\u03bba+(1-\u03bb)b,\u90a3\u9ebcx\u2208(a,b).\u8bbe\u70b9A(a,f(a)),B(b,f(b)),\u5219\u76f4\u7ebfAB\u65b9\u7a0b\u4e3a
y-f(a)=[f(b)-f(a)]/(b-a)*(x-a)(\u6211\u8bbe\u8fd9\u6761\u76f4\u7ebf\u4e3ag(x)=mx+n)
\u5c06x=\u03bba+(1-\u03bb)b\u4ee3\u5165AB\u65b9\u7a0b,\u5316\u7b80\u5f97y=\u03bbf(a)+(1-\u03bb)f(b)
\u4e5f\u5c31\u662f\u8bf4\u5728[a,b]\u4e0a\u6052\u6709f(x)\u2264g(x)
\u6839\u636e\u5b9a\u79ef\u5206\u7684\u6027\u8d28,\u222b[a,b]f(x)dx\u2264\u222b[a,b]g(x)dx
\u222b[a,b]g(x)dx=\u222b[a,b](mx+n)dx
=1/m*1/2*(mx+n)²|[a,b]
=1/2*(b-a)*[f(a)+f(b)]
\u539f\u4e0d\u7b49\u5f0f\u6210\u7acb
x=1\u4e3a\u5bf9\u79f0\u8f74\uff0c\u53731=-(a+2)/2, a=0
\u533a\u95f4[a,b]\u4e5f\u9700\u5173\u4e8eX=1\u5bf9\u79f0\uff0c
\u6240\u4ee5b=2.
。
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