Answer:
Option A
Explanation:
Given , $6y= x^{3}+2$...........(i)
and $\triangle y=8 \triangle x$
On differentiating both sides of Eq.(i) w.r.t x. we get
$\frac{6dy}{dx}=3x^{2}\Rightarrow \frac{dy}{dx}=\frac{1}{2} x^{2}$
$\because$ $\triangle y=\frac{dy}{dx}\triangle x\Rightarrow 8\triangle x=\frac{1}{2}x^{2} \triangle x$
$\Rightarrow$ $ x^{2}=16 \Rightarrow x=\pm 4$
When x=4 , 6y=$(4)^{3}$+2
$\Rightarrow$ 6y=66 $\Rightarrow$ y=11
Hence , required point is (4,11)
