巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区...巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区间(a,a+1)上
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![巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区...巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区间(a,a+1)上](/uploads/image/z/3773547-27-7.jpg?t=%E5%B7%B3%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%E7%9A%84%E5%B9%B3%E6%96%B9-8lnx%2Cg%28x%29%3D-x%E7%9A%84%E5%B9%B3%E6%96%B9%2B14x%2C%281%29%E6%B1%82f%28x%29%E5%9C%A8%281%2Cf%281%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%3B%282%29%E8%8B%A5f%28x%29%E4%B8%8Eg%28x%29%E5%9C%A8%E5%8C%BA...%E5%B7%B3%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%E7%9A%84%E5%B9%B3%E6%96%B9-8lnx%2Cg%28x%29%3D-x%E7%9A%84%E5%B9%B3%E6%96%B9%2B14x%2C%281%29%E6%B1%82f%28x%29%E5%9C%A8%281%2Cf%281%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%3B%282%29%E8%8B%A5f%28x%29%E4%B8%8Eg%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%28a%2Ca%2B1%29%E4%B8%8A)
巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区...巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区间(a,a+1)上
巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区...
巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区间(a,a+1)上均为增函数,求a的取值范围
巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区...巳知函数f(x)=x的平方-8lnx,g(x)=-x的平方+14x,(1)求f(x)在(1,f(1))处的切线方程;(2)若f(x)与g(x)在区间(a,a+1)上
f'(x)=2x-8/x
f'(1)=-6
f(1)=1
由点斜式y-f(1)=f"(1)(x-1)
y-1=-6(x-1)
6x+y-7=0
f '(x)=2x-8/x=2(x-4/x)>0 x>4/x 或x>2或-2
1、f'(x)=2x-8/x=2(x+2)(x-2)/x,k=f'(1)=-6,切点(1,1),切线是6x+y-7=0;
2、g(x)=-x²+14x在(-∞,7]上增,f(x)在[2,+∞)上增,则2≤a≤6。
1
f'(x)=2x-8/x
f'(1)=2-8=-6,f(1)=1
y-1=-6(x-1)
切线y=-6x+7
2
f(x)=x^2-8lnx g(x)=-x^2+14x g'(x)=-2x+14≥0 x≤7
f'(x)=2x-8/x≥ 0,x≥2或x≤-2
2≤x≤7, a≥2, a+1≤7,a≤6
2≤a≤6