# What is the equation of the line normal to f(x)=(3x-1)(2x+4) at x=0?

Mar 17, 2016

$10 y = - x + 40$

#### Explanation:

Differentiate the formula to find the slope $m$. The line normal to the function is then $- \frac{1}{m}$. Given the point through which it passes, the equation of the line can then be calculated.
$f \left(x\right) = \left(3 x - 1\right) \left(2 x + 4\right)$
$f \left(x\right) = 6 {x}^{2} + 10 x - 4$
$f ' \left(x\right) = 12 x + 10$

At $x = 0$, $f ' \left(x\right) = 10$
$\therefore - \frac{1}{m} = - \frac{1}{10}$

At $x = 0$, $f \left(x\right) = 4$
$4 = - \frac{x}{10} + c$
$\therefore c = 4$

the equation of the normal is $10 y = - x + 40$