Question

If y = x2 - 2x + 3 then what will be the minimum value of y ?
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Answer 1

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Ok cool … So, we have:

y=x2−2x+3y=x2−2x+3

OR,

y=(x-1)^2 + 2

Clearly, (x-1)^2>=0 .

So,

y>=2 .

In the view of Calculus :

Differentiation on both sides yields..

y’=(2x-2)

y’’=2>0 (So, it only has a minima (Upward Concave Parabola) )

Equating it to zero gives x=1 .

Again giving us minimum at x=1 when y=2.

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