中四級M1數(4)

1(a) f(x) = x(x^2 + k)^(1/2)f'(x) = (x^2 + k)^(1/2) + x^2(x^2 + k)^(-1/2)f'(2) = 13/3(4 + k)^(1/2) + 4(4 + k)^(-1/2) = 13/3令(4 + k)^(1/2) = yy + 4/y = 13/33y^2 - 13y + 12 = 0(3y - 4)(y - 3) = 0y = 4/3 或 3(b) f''(2) 的值不會相同﹐因為常數k在根號內﹐兩次導數後不會被消去26 (3x - 1)/f(x) 的導數為[3f(x) - (3x - 1)f'(x)]/[f(x)]^2在0時﹐導數 = [3(-2) - (-1) * 3]/(-2)^2 = -3/427 f(xf(x))的導數為f'(xf(x)) * [xf'(x) + f(x)]當x = 1時﹐導數為f'(-1) * [1 + (-1)] = 0

1A錯誤~其他正確.......

2013-12-08 14:21:58 補充：
1a)

(y-3)=0
即(4+k)^1/2 - 3 = 0
4+k=9
k=5

3y-4=0
y=4/3
(4+k)^1/2=4/3
k=-20/9

感謝1號回答的協助~