定义在R上的函数f(x)满足,如果对任意X1,X2∈R,都有f(x1+x2/2)≦1/2,[f(x1),f(x2)],则称函数f(x)是R上的凹函数.已知函数f(x)=ax2+x(a∈R且a≠0)求证:(1)当a>0时,函数f(x)是凹函数(2)如果x属于[0,1],|f(x
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![定义在R上的函数f(x)满足,如果对任意X1,X2∈R,都有f(x1+x2/2)≦1/2,[f(x1),f(x2)],则称函数f(x)是R上的凹函数.已知函数f(x)=ax2+x(a∈R且a≠0)求证:(1)当a>0时,函数f(x)是凹函数(2)如果x属于[0,1],|f(x](/uploads/image/z/6083998-70-8.jpg?t=%E5%AE%9A%E4%B9%89%E5%9C%A8R%E4%B8%8A%E7%9A%84%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3%2C%E5%A6%82%E6%9E%9C%E5%AF%B9%E4%BB%BB%E6%84%8FX1%2CX2%E2%88%88R%2C%E9%83%BD%E6%9C%89f%28x1%2Bx2%EF%BC%8F2%29%E2%89%A61%2F2%2C%5Bf%28x1%29%2Cf%28x2%29%5D%2C%E5%88%99%E7%A7%B0%E5%87%BD%E6%95%B0f%28x%29%E6%98%AFR%E4%B8%8A%E7%9A%84%E5%87%B9%E5%87%BD%E6%95%B0.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dax2%2Bx%28a%E2%88%88R%E4%B8%94a%E2%89%A00%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%281%29%E5%BD%93a%3E0%E6%97%B6%2C%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E6%98%AF%E5%87%B9%E5%87%BD%E6%95%B0%EF%BC%882%EF%BC%89%E5%A6%82%E6%9E%9Cx%E5%B1%9E%E4%BA%8E%5B0%2C1%5D%2C%7Cf%28x)
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