Answer:
Option A
Explanation:
The curve $y=ax^{3}+bx+4$ is passes through (2,14)
$\therefore$ $14=a(2)^{3}+b(2)+4$
$\Rightarrow$ $14=8a+2b+4$
$\Rightarrow$ $5=4a+b$ ........(i)
Slope of tangent to the curve $y=ax^{3}+bx+4$
i.e, $\frac{dy}{dx}= 3ax^{2}+b$
$\Rightarrow$ $\left(\frac{dy}{dx}\right)_{(2,14)}=3a(2)^{2}+b$
$\Rightarrow$ $21=12a+b$ .........(ii)
$\left[\because \frac{dy}{dx}=21\right]$
Solving Eqs.(i) and (ii) , we get
a=2, b=-3
