※ 引述《victor7935 (victor)》之铭言： : 1. : Find A and B given that the function : f(x) = { x^3 , x 小於等於1 : { Ax +B , x> 1 应该有说函数是连续且可微分的吧? - f'(x->1 ) = 3 + f'(x->1 ) = A A = 3 - f(x->1 ) = 1 + f(x->1 ) = A + B = 3 + B B = -2 : 2.Find conditions on a,b,c,d which guarantee that the graph : of the cubic p(x)=ax^3+bx^2+cx+d cubic 三次方 : (1.) exactly two horizontal tangents. a =/= 0 因为cubic p' = 3ax^2 + 2bx + c 因为有两条水平线 表示有两个"相异"x使得p'(x) = 0 所以判别式要 > 0 4b^2 - 12ac > 0 => b^2 > 3ac : 2 2 : 3.Express d y/d x : (a) 4tany = x^3 题目的意思是要你用x的函数来表达y'' 4(secy)^2 * y' = 3x^2 8(secy)(secy)(tany)y'y' + 4(secy)^2 y'' = 6x 8(secy)^2 (tany) 9x^4 => ----------------------- + 4(secy)^2 y'' = 6x 16 (secy)^4 9 x^4 tany => --------------------- + 4 [1 + (tany)^2] y'' = 6x 4 [1 + (tany)^2] 9 x^4 x^3 => -------------------- + 4 [1 + x^6 /16]y'' = 6x 16 [1 + x^6 /16] 移项後就等式左边y'' 右边都是x的函数 即为所求 --

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