What is the equation of the normal line of $f(x)= -2x^3-10x$ at $x=2$ ?

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Answer 1 · 2017-01-12T10:53:57

The equation of the normal line is:

$y = x/34 -36-1/17$

The equation of the line normal to the graph $y=f(x)$ in the point $(bar x, f(bar x))$ is given by:

$y=f(bar x)-1/(f'(barx)) (x - barx)$

In our case $bar x = 2$ and:

$f(x) = -2x^3-10x => f(2) = -36$

$f'(x) = -6x^2-10 => f'(2) = -34$

So the equation of the normal line is:

$y = -36 +1/34(x-2) = x/34 -36-1/17$

What is the equation of the normal line of f(x)= -2x^3-10x f(x)= -2x^3-10x at x=2 x=2 ?