[微分] 問題請教...

[victor7935 (victor)]

1.
 Find  A and B  given that the function

                          f(x) = {   x^3  ,  x 小於等於1
                                 { Ax +B  ,  x> 1

2.Find conditions on a,b,c,d which guarantee that the graph

 of the cubic p(x)=ax^3+bx^2+cx+d

   (1.)  exactly two horizontal tangents.

           2     2
3.Express d y/d x


  (a) 4tany = x^3





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推 GBRS:3.4tany = x^3 => y=arctan(x^3/4)...總之容
→ GBRS:易看出y是x的函數
推 GBRS:或者先一次微分=>4sec^2y*y'=3x^2=>再利用平
→ GBRS:方關係sec^2y=1+tan^2y=1+(x^3/4)^2可整理出
→ GBRS:y'是x的函數即可再微分一次...