(1)f(X)=ax^2-4b+1,a∈{-1,1,2,3,4,5},b{-2,-1,1,2,3,4}f(x)在(-1,+∞)上为增函数的概率(2)(a,b)是{x+y-8≤0,x≥0,y≥0内随机点,则f(x)在(1,+∞)上为增函数的概率
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![(1)f(X)=ax^2-4b+1,a∈{-1,1,2,3,4,5},b{-2,-1,1,2,3,4}f(x)在(-1,+∞)上为增函数的概率(2)(a,b)是{x+y-8≤0,x≥0,y≥0内随机点,则f(x)在(1,+∞)上为增函数的概率](/uploads/image/z/8946654-6-4.jpg?t=%EF%BC%881%EF%BC%89f%28X%29%3Dax%5E2-4b%2B1%2Ca%E2%88%88%7B-1%2C1%2C2%2C3%2C4%2C5%7D%2Cb%7B-2%2C-1%2C1%2C2%2C3%2C4%7Df%28x%29%E5%9C%A8%28-1%2C%EF%BC%8B%E2%88%9E%29%E4%B8%8A%E4%B8%BA%E5%A2%9E%E5%87%BD%E6%95%B0%E7%9A%84%E6%A6%82%E7%8E%87%EF%BC%882%EF%BC%89%EF%BC%88a%2Cb%EF%BC%89%E6%98%AF%7Bx%2By-8%E2%89%A40%2Cx%E2%89%A50%2Cy%E2%89%A50%E5%86%85%E9%9A%8F%E6%9C%BA%E7%82%B9%2C%E5%88%99f%EF%BC%88x%EF%BC%89%E5%9C%A8%EF%BC%881%2C%EF%BC%8B%E2%88%9E%EF%BC%89%E4%B8%8A%E4%B8%BA%E5%A2%9E%E5%87%BD%E6%95%B0%E7%9A%84%E6%A6%82%E7%8E%87)
(1)f(X)=ax^2-4b+1,a∈{-1,1,2,3,4,5},b{-2,-1,1,2,3,4}f(x)在(-1,+∞)上为增函数的概率(2)(a,b)是{x+y-8≤0,x≥0,y≥0内随机点,则f(x)在(1,+∞)上为增函数的概率
(1)f(X)=ax^2-4b+1,a∈{-1,1,2,3,4,5},b{-2,-1,1,2,3,4}f(x)在(-1,+∞)上为增函数的概率(2)(a,b)是{x+y-8≤0,x≥0,y≥0内随机点,则f(x)在(1,+∞)上为增函数的概率
(1)f(X)=ax^2-4b+1,a∈{-1,1,2,3,4,5},b{-2,-1,1,2,3,4}f(x)在(-1,+∞)上为增函数的概率(2)(a,b)是{x+y-8≤0,x≥0,y≥0内随机点,则f(x)在(1,+∞)上为增函数的概率
(1) (a,b)对的选择共有6*6=36种.
f(x)在(-1,+∞)上为增函数==>抛物线f(x)的开口向上,对称轴位x=2b/a位于(-1,+∞)的左侧,即 a>0且2b/a≤-1.==>a>0且b≤-a/2.==>(a,b)可取(1,-2),(1,-1),(2,-2),(2,-1),(3,-2),(4,-2);有6种.
故所求概率为 6/36=1/6.
(2) 依题意,(a,b)的选择为可行域问题,用面积法求解.
以a为x轴,b为y轴,则a,b满足{a+b-8≤0,a>=0,b>=0}围成的面积为一直角三角形,面积为32.
f(x)在(1,+∞)上为增函数==>抛物线f(x)的开口向上,对称轴位x=2b/a位于(1,+∞)的左侧,即 a>0且2b/a≤1,所围成的面积为32/3.
故所求概率为 (32/3)/32=1/3 .
题目可能有误,f(X)是否应为ax^2-4bx+1
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