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

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Answer 1 · 2017-05-25T22:58:11

$y = x/18 + 41 + 5/6$

$f(x) = 2x^2 - 6x + 6$

$f'(x) = 4x - 6$

$f'(-3) = -12 - 6 = - 18$

We want a line $y = 1/18 x + b$ , where $(-3, f(-3))$ is one of its points.

$f(-3) = 2*9 + 18 + 6 = 42$

$42 = 1/18 (-3) + b$

$b = 42 - 1/6 = 41 + 5/6$

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