The point on the curve y=x^2+7 nearest to point (3, 7) is:

The correct answer is Option (1) → (1, 8)

$y = x^2 + 7$

$D^2 = (x-3)^2 + (x^2+7-7)^2 = (x-3)^2 + x^4$

$\frac{d}{dx}(D^2) = 2(x-3) + 4x^3$

$= 2x - 6 + 4x^3 = 0$

$2x^3 + x - 3 = 0$

$x=1 \Rightarrow 2(1)^3+1-3=0$

$y = 1^2 + 7 = 8$

$\text{Nearest point} = (1,8)$