What is the equation of the normal line of $f(x)=5x^3+x^2-5x-2$ at $x=2$ ?

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Answer 1 · 2016-05-16T15:51:48

$f(x) = 5x^3+x^2-5x-2$

At $x=2$ , we have $y=f(2) = 44-12 = 32$

$f'(x) = 15x^2+2x-5$ , so the slope of the tangent line is $f'(2) = 64-5 = 59$

The normal line is perpendicular to the tangent, so its slope is $-1/59$

An equation for the normal line is $y=32-1/59(x-2)$ .

This can also be written $y=-1/59x+32 2/59$ .

What is the equation of the normal line of f(x)=5x^3+x^2-5x-2f(x)=5x^3+x^2-5x-2 at x=2x=2?