For $f(x)=x-x^3-x^2$ what is the equation of the tangent line at $x=12$ ?

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Answer 1 · 2018-05-05T03:11:49

$f(12)=12-1728-144=-1860$
So the point of tangency is $(x_0,y_0)=(12,-1860)$ .

Since $f'(x)=1-3x^2-2x$ , the slope of the tangent line at $x=12$ is $m=f'(12)=1-432-24=-455$ .

So the equation of the tangent line at the point $(12,-1860)$ is

$y-y_0 = m(x-x_0)$

$y+1860=-455(x-12)$

$y+1860=-455x+5460$

$y=-455x+3600$

For f(x)=x-x^3-x^2f(x)=x-x^3-x^2 what is the equation of the tangent line at x=12x=12?