等比数列{an}中,a8=4,函数f(x)=x(x-a1)•(x-a2)•…•(x-
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等比数列{an}中,a8=4,函数f(x)=x(x-a1)•(x-a2)•…•(x-a8),则f′(0)=
![等比数列{an}中,a8=4,函数f(x)=x(x-a1)•(x-a2)•…•(x-](/uploads/image/z/8052346-10-6.jpg?t=%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Ca8%EF%BC%9D4%2C%E5%87%BD%E6%95%B0f%28x%29%EF%BC%9Dx%28x%EF%BC%8Da1%29%26%238226%3B%28x%EF%BC%8Da2%29%26%238226%3B%E2%80%A6%26%238226%3B%28x%EF%BC%8D)
f'(x)=f(x)/x+f(x)/(x-a1)+...+f(x)/(x-a8)
当x=0时,f(x)/(x-a1),f(x)/(x-a2),...f(x)/(x-a8)都含x项,故都等于0
所以f'(0)=(-a1)*(-a2)*...*(-a8)
=a1*a2*...*a8
=(a1*a8)^4
=a1^4*a8^4
=a1^4*4^4
=256a1^4
不知a1=?等不下去啦.
当x=0时,f(x)/(x-a1),f(x)/(x-a2),...f(x)/(x-a8)都含x项,故都等于0
所以f'(0)=(-a1)*(-a2)*...*(-a8)
=a1*a2*...*a8
=(a1*a8)^4
=a1^4*a8^4
=a1^4*4^4
=256a1^4
不知a1=?等不下去啦.
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