已知f0(x)=xe^x,定义fn(x)=f'(n-1)(x) x属于N,试归纳出fn(x)的表达式
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已知f0(x)=xe^x,定义fn(x)=f'(n-1)(x) x属于N,试归纳出fn(x)的表达式
求fn(x)的极小值,点Pn(Xn,yn)
求fn(x)的极小值,点Pn(Xn,yn)
![已知f0(x)=xe^x,定义fn(x)=f'(n-1)(x) x属于N,试归纳出fn(x)的表达式](/uploads/image/z/18246631-31-1.jpg?t=%E5%B7%B2%E7%9F%A5f0%28x%29%3Dxe%5Ex%2C%E5%AE%9A%E4%B9%89fn%28x%29%3Df%27%28n-1%29%28x%29+x%E5%B1%9E%E4%BA%8EN%2C%E8%AF%95%E5%BD%92%E7%BA%B3%E5%87%BAfn%EF%BC%88x%EF%BC%89%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F)
f0(x) = xe^x
f1(x) = f'(0)(x)
=(x+1)e^x
f2(x) = f'(1)x
= (x+2)e^x
...
...
fn(x) = f'(n-1)x
= (x+n)e^x
再问: 求fn(x)的极小值,点Pn(Xn,yn) 求下这个吧...说实话,我是没看懂- -
再答: fn(x) = (x+n)e^x f'n(x) = (x+n+1)e^x =0 x= -(n+1) f''n(x) = (x+n+2)e^x f''n(-(n+1)) = e^(-(n+1)) >0 ( min ) min fn(x) = fn(-n+1)) = -e^(-(n+1)) Pn(xn,yn) = (-(n+1), -e^(-(n+1)))
再问: 3Q
f1(x) = f'(0)(x)
=(x+1)e^x
f2(x) = f'(1)x
= (x+2)e^x
...
...
fn(x) = f'(n-1)x
= (x+n)e^x
再问: 求fn(x)的极小值,点Pn(Xn,yn) 求下这个吧...说实话,我是没看懂- -
再答: fn(x) = (x+n)e^x f'n(x) = (x+n+1)e^x =0 x= -(n+1) f''n(x) = (x+n+2)e^x f''n(-(n+1)) = e^(-(n+1)) >0 ( min ) min fn(x) = fn(-n+1)) = -e^(-(n+1)) Pn(xn,yn) = (-(n+1), -e^(-(n+1)))
再问: 3Q
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