F(x)=2x-x^2/2 g(x)= logaX (a>0且a不等于1)h(x)=f(x)-g(x)在定义域上为减函数且h'(x)存在零点(1)求实数a的值(2)y=P(x)与y=g(x)关于直线y=x对称A(x1,y1)B(x2,y2),x1小于x2A,B为y=P(x)上的两点P'(x0)=
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![F(x)=2x-x^2/2 g(x)= logaX (a>0且a不等于1)h(x)=f(x)-g(x)在定义域上为减函数且h'(x)存在零点(1)求实数a的值(2)y=P(x)与y=g(x)关于直线y=x对称A(x1,y1)B(x2,y2),x1小于x2A,B为y=P(x)上的两点P'(x0)=](/uploads/image/z/3737500-52-0.jpg?t=F%28x%29%3D2x-x%5E2%2F2+g%28x%29%3D+logaX+%28a%3E0%E4%B8%94a%E4%B8%8D%E7%AD%89%E4%BA%8E1%29h%28x%29%3Df%28x%29-g%28x%29%E5%9C%A8%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%8A%E4%B8%BA%E5%87%8F%E5%87%BD%E6%95%B0%E4%B8%94h%27%EF%BC%88x%EF%BC%89%E5%AD%98%E5%9C%A8%E9%9B%B6%E7%82%B9%281%29%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89y%3DP%28x%29%E4%B8%8Ey%3Dg%EF%BC%88x%EF%BC%89%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BFy%3Dx%E5%AF%B9%E7%A7%B0A%EF%BC%88x1%2Cy1%EF%BC%89B%EF%BC%88x2%2Cy2%EF%BC%89%2Cx1%E5%B0%8F%E4%BA%8Ex2A%2CB%E4%B8%BAy%3DP%28x%EF%BC%89%E4%B8%8A%E7%9A%84%E4%B8%A4%E7%82%B9P%27%EF%BC%88x0%EF%BC%89%3D)
F(x)=2x-x^2/2 g(x)= logaX (a>0且a不等于1)h(x)=f(x)-g(x)在定义域上为减函数且h'(x)存在零点(1)求实数a的值(2)y=P(x)与y=g(x)关于直线y=x对称A(x1,y1)B(x2,y2),x1小于x2A,B为y=P(x)上的两点P'(x0)=
F(x)=2x-x^2/2 g(x)= logaX (a>0且a不等于1)
h(x)=f(x)-g(x)在定义域上为减函数且h'(x)存在零点
(1)求实数a的值
(2)y=P(x)与y=g(x)关于直线y=x对称A(x1,y1)B(x2,y2),x1小于x2
A,B为y=P(x)上的两点P'(x0)=(y1-y2)/(x1-x2)
判断x0,x1,x2的大小并证明
F(x)=2x-x^2/2 g(x)= logaX (a>0且a不等于1)h(x)=f(x)-g(x)在定义域上为减函数且h'(x)存在零点(1)求实数a的值(2)y=P(x)与y=g(x)关于直线y=x对称A(x1,y1)B(x2,y2),x1小于x2A,B为y=P(x)上的两点P'(x0)=
h'(x)=2-x-1/(xlna)
h'(x)=0=2-x-1/(xlna)
即:2x-x² -1/lna=0
h(x)=f(x)-g(x)在定义域上为减函数☞△≤0☞lna≤1
对m=2-x-1/(xlna)☞m'=-1+(1/lna)*(1/x²)=0☞x=√(1/lna)
因为h'(x)≤0,在h'(x)有零点所以最大值h'(√(1/lna))≥0解得lna≥1
当且仅当lna=1成立也就是a=e
y=P(x)与y=g(x)关于直线y=x对称也就是它们互为反函数
题目意思不懂