The correct option is B 14
y=x3+k
dydx=3x2=34 ⇒ x=±12
When x=12 ,y=38, and (12,38) lies on the curve y=x3+k
So, 38=18+k ⇒k=14
When x=−12,y=−38, and (−12,−38) lies on the curve
So, −38=−18+k⇒k=−14
But we need the point lying in the first quadrant. Hence, k=14