What is the equation of the normal line of $f (x) = x^{2} - x + \frac{1}{x}$ $f(x)=x^2-x+1/x$ at $x = 2$ $x = 2$ ?

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Answer 1 · 2016-12-02T10:39:35

The equation is:

$y (x) = - \frac{4}{11} x + \frac{71}{22}$ $y(x) =-4/11x+71/22$

The general formula of the normal line to a curve is:

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

Given:

$f(x) = x^2-x+1/x$
$f'(x) =2x-1-1/x^2$

For $x=2$ :

$f(x)|_(x=2) =5/2$

$f'(x)|_(x=2) =11/4$

So:

$y(x) =5/2-4/11(x-2)=-4/11x+71/22$

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What is the equation of the normal line of f(x)=x^2-x+1/xf(x)=x2−x+1xf(x)=x^2-x+1/x at x = 2x=2x = 2?