Show the steps very clearly.
1. If f(x) = (x - 3)^2 + (x - 4)^2, find the minimum value of f(x).
A maths (2)
2007-09-15 10:08 pm
回答 (4)
2007-09-15 10:20 pm
參考: Myself~~~
2007-09-15 10:27 pm
f(x) = x^2 - 6x +9+x^2-8x+16
= 2x^2 - 14x + 25
f ' (x) = 4x - 14
x = 3.5
所以 : f(3.5) = (3.5-3) ^2 + (3.5-4) ^2
= 0.5^2 + (-0.5) ^2
= 0.25+0.25
= 0.5
the minimum value of f(x) is 0.5
= 2x^2 - 14x + 25
f ' (x) = 4x - 14
x = 3.5
所以 : f(3.5) = (3.5-3) ^2 + (3.5-4) ^2
= 0.5^2 + (-0.5) ^2
= 0.25+0.25
= 0.5
the minimum value of f(x) is 0.5
2007-09-15 10:26 pm
1) f(x) = (x - 3)^2 + (x - 4)^2
= x^2 -6x +9 +x^2 -8x +16
= 2x^2 -14x +25
= 2( x^2 -7x +(7/2)^2 -(7/2)^2 +25/2 )
= 2( x-3.5 )^2 + 0.5
min.of f(x) = min. of 2( x-3.5 )^2 + min. of 0.5
= 0 + 0.5
= 0.5
.'. the min. value of f(x) is 0.5 at x = 3.5 .
= x^2 -6x +9 +x^2 -8x +16
= 2x^2 -14x +25
= 2( x^2 -7x +(7/2)^2 -(7/2)^2 +25/2 )
= 2( x-3.5 )^2 + 0.5
min.of f(x) = min. of 2( x-3.5 )^2 + min. of 0.5
= 0 + 0.5
= 0.5
.'. the min. value of f(x) is 0.5 at x = 3.5 .
參考: myself
2007-09-15 10:21 pm
f(x)=(x^2-6x+9)+(x^2-8x+16)
=2x^2-14x+25
=2(x^2-7x+49/4)-49/2+25
=2(x-7/2)^2+1/2
if x=7/2 ,
the minimum value of f(x)=1/2
=2x^2-14x+25
=2(x^2-7x+49/4)-49/2+25
=2(x-7/2)^2+1/2
if x=7/2 ,
the minimum value of f(x)=1/2
參考: me
收錄日期: 2021-04-13 14:01:53
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https://hk.answers.yahoo.com/question/index?qid=20070915000051KK02278