Question

If the slope of line, passing through the origin which is tangent to the curve $y=x^3+x+16$ is $m$, then the value of $m-4$ is

Answer 1

$y=x^3+x+16$
${\left(\frac{dy}{dx}\right)}_{(x_1,y_1)}=3x_1^2+1$
$\Rightarrow 3x_1^2+1=\frac{y_1}{x_1}$
$\Rightarrow 3x_1^3+x_1=x_1^3+x_1+16$
$\Rightarrow 2x_1^3=16$
$\Rightarrow x_1=2\Rightarrow y_1=26$
$\therefore m=13$
$\Rightarrow m-4=9$