Re: [考古] 91逢甲
※ 引述《kusorz (^~^)》之銘言：
: suppose that g is the inverse function of f.
: if f(3)=2,f'(3)=1/9 and f''(3)=-5,then g''(2)=?
g''(x)= -f''(g(x)) / [f'(g(x))]^3
證明如下
g'(x) = 1 / f'(g(x))
g''(x) = - [f'(g(x)]' / [f'(g(x))]^2
= - f''(g(x))*g'(x) / [f'(g(x))]^2
= - f''(g(x)) / [f'(g(x))]^3
f(3)=2 , g(2)=3
g''(2) = - f''(g(2)) / [f'(g(2))]^3
= - f''(3) / [f'(3)]^3
= - (-5) / (1/9)^3
= 3645
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