Find the minimum value of f(x)=x^2-x+1÷x^2+x+1
Sadu REDDI SAIKUMAR REDDY , 12 Years ago
Grade 11
Differential Calculus> Find the minimum value of f(x)=x^2-x+1÷x^...
2 Answers
Sher Mohammad
f'(x)=0 imply (2x-1)(x^2+x+1) - (2x+1)(x^2-x+1)=0
solving gives, x=1
lokesh palingi
y=(x^2-x+1)/(x^2+x+1)
yx^2+yx+y=x^2-x+1
(y-1)x^2+(y+1)x+y-1=0
since x belong to R
Therefore, Discriminant>=0
(y+1)^2-4(y-1)(y-1)>=0
y^2+2y+1-4y^2+8y-4>=0
-3y^2+10y-3>=0
3y^2-10y+3<=0
(y-3)(3y-1)<=0
y belong to 1/3 to 3 so minimum value is 1/3
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