What is the equation of the normal line of f(x)= 3x - 2x^2 at x=1?

1 Answer

$y = x$

Explanation:

Given: $y = 3 x - 2 {x}^{2}$

Computing for the ordinate $y = 1$

our point is $\left(1 , 1\right)$

$f ' \left(x\right)$ = slope

$f ' \left(1\right) = - 1$

the negative reciprocal of the slope is needed foe the Normal line.

so for the normal line $m = - \frac{1}{f ' \left(1\right)} = - \frac{1}{-} 1 = 1$

$y - {y}_{1} = m \left(x - {x}_{1}\right)$