Let f(x) = x^(2)-8x and g(x) = x^(2)+4x-7. Find the minimum value of f(x)+g(x).
The ans is -9
*pls show the workings.
University Maths Question
2010-07-28 5:52 am
回答 (2)
2010-07-28 6:54 am
✔ 最佳答案
let y= f(x)+g(x) = [x^2+4x-7] + [x^2-8x]=2x^2-4x-7
y'=4x-4
when f(x) is at the extreme, y' =0
i.e. x = 1 when f(x) is at the extreme
y'' = 4 > 0
so it is a minium
so minimum of f(x) + g(x) = f(1) + g(1) = -9
2010-07-28 10:13 pm
Let f(x) = x^(2)-8x and g(x) = x^(2)+4x-7. Find the minimum value of f(x)+g(x).
let y=f(x)+g(x)
y=x^2-8x+x^2+4x-7
y=2x^2-4x-7
y=2(x^2-2x+1)-9
y=2(x-1)^2-9
we know
(x-1)^2>=0
2(x-1)^2>=0
(x-1)^2-9>=-9
y>=-9
so minimum value is -9
use the vertex form of equation y=a(x-h)^2+k
where (h,k) is the maximun or minimun depends on the value of a
let y=f(x)+g(x)
y=x^2-8x+x^2+4x-7
y=2x^2-4x-7
y=2(x^2-2x+1)-9
y=2(x-1)^2-9
we know
(x-1)^2>=0
2(x-1)^2>=0
(x-1)^2-9>=-9
y>=-9
so minimum value is -9
use the vertex form of equation y=a(x-h)^2+k
where (h,k) is the maximun or minimun depends on the value of a
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