The maximum value of f(x)=-x^2+2x+4,\ x∈ R (set of real numbers) is

The correct answer is Option (2) → 5

Completing the square,

    \( f(x)=-(x^{2}-2x)+4 \)

    \( =-(x-1)^{2}+1+4 \)

    \( =5-(x-1)^{2} \)

The term \( (x-1)^{2} \) is never negative, so \( f(x)\le 5 \).

The value 5 is reached at \( x=1 \), so the maximum value is 5.