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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

MuraliKrishna Medavaram
askIITians Faculty 33 Points
7 years ago

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Thanks and Regards,
M.MURALIKRISHNA
askIITians faculty
bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 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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