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iam无痕

铜虫 (初入文坛)

[求助] 求一函数的系数,急! 已有2人参与

y=0.5×[1-(tanh[C(2x-1)]/tanh(C) )]
当x=1时,这个函数的一阶导数取最大值,求C的值。
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feixiaolin

荣誉版主 (文坛精英)

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C可能无唯一值
2楼2015-08-17 21:10:35
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wurongjun

专家顾问 (职业作家)

【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
感谢参与,应助指数 +1
iam无痕(feixiaolin代发): 金币+10 2015-08-18 13:16:44
feixiaolin: 金币+3 2015-08-20 11:53:32
有三个解!
>> solve((x*tanh(x)^2-tanh(x)+x),'x')
ans =
0
>> syms C x
>> f=0.5*(1-(tanh(C*(2*x-1))/tanh(C)))
f =
1/2-1/2*tanh(C*(2*x-1))/tanh(C)
>> ddf1=diff(df1,C,1)
ddf1 =
(1-tanh(C)^2)*(tanh(C)+1)*C/tanh(C)+(tanh(C)-1)*(1-tanh(C)^2)*C/tanh(C)+(tanh(C)-1)*(tanh(C)+1)/tanh(C)-(tanh(C)-1)*(tanh(C)+1)*C/tanh(C)^2*(1-tanh(C)^2)
>> df=diff(f,x,1)
df =
-(1-tanh(C*(2*x-1))^2)*C/tanh(C)
>> dfc=factor(subs(df,x,1))
dfc =
(tanh(C)-1)*(tanh(C)+1)*C/tanh(C)
>> ddfc=diff(df1,C,1)
ddfc =
(1-tanh(C)^2)*(tanh(C)+1)*C/tanh(C)+(tanh(C)-1)*(1-tanh(C)^2)*C/tanh(C)+(tanh(C)-1)*(tanh(C)+1)/tanh(C)-(tanh(C)-1)*(tanh(C)+1)*C/tanh(C)^2*(1-tanh(C)^2)
>> factor(ddfc)
ans =
-(tanh(C)-1)*(tanh(C)+1)*(C*tanh(C)^2-tanh(C)+C)/tanh(C)^2
>> jc1=solve(tanh(x)-1,'x')
jc1 =
193.35532743389497808484386881993
>> jc2=solve(tanh(x)+1,'x')
jc2 =
-188.20974064478531378512841977016
>> jc3=solve(x*tanh(x)^2-tanh(x)+x,'x')
jc3 =
0
>>
善恶到头终有报,人间正道是沧桑.
3楼2015-08-17 22:22:02
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peterflyer

木虫之王 (文学泰斗)

peterflyer


【答案】应助回帖

★ ★ ★ ★ ★
感谢参与,应助指数 +1
iam无痕(feixiaolin代发): 金币+5 2015-08-20 11:53:21
y=0.5*{1-{tanh[C(2x-1)]/tanh(C) }}
y'=0.5*{-{1/Cosh[C*(2*x-1)]}^2*2*C/tanh(C)}
x=1时,
Q(C)=y'=-C/tanh(C)*1/[Cosh(C)]^2
       = - 4*C/{exp(2*C)-exp(-2*C)}
Q(C)对C求导数,得:
dQ/dC=-4{1*[exp(2*C)-exp(-2*C)]-C*[2*exp(2*C)+2*exp(-2*C)]}/{exp(2*C)-exp(-2*C)}^2 ≡ 0
  若exp(2*C)-exp(-2*C)≠0
  则:[1-2*C]*exp(2*C)-[1+2*C]*exp(-2*C)=0
exp(4*C)=(1+2*C)/(1-2*C)
解得C=0
4楼2015-08-19 16:35:41
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