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CUET
-- Applied Mathematics - Section B2
Calculus
If x is real, the minimum value of $f(x)=x^2-8x+20 $ is :
4
1
2
3
The correct answer is Option (1) → 4
$f(x)=x^2-8x+20$
$f(x)=(x^2-8x+16)+4=(x-4)^2+4$
$(x-4)^2≥0$
Since $(x-4)^2≥0\,∀\,x$, minimum value $(x-4)^2=0$, i.e. at $x=4$
$f(4)=0+4=4$