Find the maximum and the minimum values, if any, without using derivatives of the following functions: `f(x)=4x^2-4x+4` on `R`

Explanation

Given,

f(x)=`4x^2-4x+4`

f(x)=`4x^2 −4x+1+3`

`∴f(x)=(2x−1)^2 +3`

we have, `(2x−1)^2 ≥0 for all x∈R`

⇒(`2x−1)^2+3≥0+3 for all x∈R`

`∴f(x)≥3 for all x∈R`

`∴x=3` is the minimum value.
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