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

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Answer 1 · 2016-03-23T23:37:48

$y-23=1/30 (x+2)$

First find the slope of the tangent line at the given point. It would be f' (-2).

Thus find $f'(x) =-6x^2 +2x -2 -> f'(-2)= -30$
The slope of the normal would be $1/30$

At x=-2, f(x) would be 16+4+4-1 =23. The given point is this (-2, 23)

Equation of the normal line, in point slope form would be

$y-23=1/30 (x+2)$

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