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Find the minimum value of f(x) = x2??x+1 x2+x+1.

Find the minimum value of f(x) = x2??x+1
x2+x+1.

Grade:10

2 Answers

sudhir pal
askIITians Faculty 26 Points
10 years ago
if this expression mean f()x = x2+x+1
for minimum value would occur where d(f(x))/dx =0 and d2f(x)/dx2 >0
d(f(x))/dx = 2x+1 =0 ; x= -1/2
d2f(x)/dx2 = 2 which is always greater than 0
minimum value occur at x = -1/2
minimum value of f(x) = (-1/2)2-1/2 +1 = 3/4



Thanks & Regards
Sudhir,
askIITians Faculty
Qualification.
IIT Delhi

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
10 years ago 
f(x) =x²-x+1/x²+x+1 = (x²+x+1- 2x )/x²+x+1
Hence, f(x) = 1 - 2x/x²+x+1
df(x)/dx = 0
x = 1, -1
Now find the value of d/dx(df(x)/dx) at x = 1,-1
For x = +1, it is positive. Hence there is a minima at x = +1.
Therefore Minimum value of f(x) is at x=+1 which is f(+1) = 1/3

Thanks & Regards
Bharat Bajaj,
askIITians Faculty
Qualification.
IIT Delhi

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