Discussion Forum

 If the slope  of the tangent of the curve $y=ax^{3}+bx+4$ at (2,14)  is 21, then the values  of a and b respectively

Answer:

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