meili 发表于 2022-10-27 15:42:39

【已知函数f(x)满足f(x)=f′(1)ex−1−f(0)x+12x2.(Ⅰ)求f(x)的解析式:(Ⅱ)求f(x)的单调区间.】

<p>问题:【已知函数f(x)满足f(x)=f′(1)ex−1−f(0)x+12x2.(Ⅰ)求f(x)的解析式:(Ⅱ)求f(x)的单调区间.】
<p>答案:↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">聂志强的回答:<div class="content-b">网友采纳  (I)f′(x)=f′(1)ex-1-f(0)+x,令x=1得f′(1)=f′(1)-f(0)+1,解得f(0)=1.∴f(x)=f′(1)ex−1−x+12x2.令x=0,得f′(1)=e,∴f(x)=ex−x+12x2.(II)设g(x)=f′(x)=ex-1+x,则g′(x)=e...
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