Discussion Forum

The point of the curve  $6y= x^{3}+2$  at which  y-coordinate is changing 8 times as fact  as x-coordinate is 

Answer:

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)