What is the equation of the tangent line of $f (x) = \frac{1}{2 x} + 4$ $f(x)=1/(2x)+4$ at $x = 2$ $x=2$ ?

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Answer 1 · 2015-12-01T15:54:26

$y = \frac{1}{8} x + 4$ $y=1/8x+4$

The slope of the tangent line at the point $(2, \frac{17}{4})$ $(2,17/4)$ is $f'(2)$ .

To find the derivative, the easiest way is to rewrite $f(x)$ as such:

$f(x)=1/2x^-1+4$

Recall that $d/dx[x^n]=nx^(n-1)$ .

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

Thus, $f'(2)=-1/(2((-2)^2))=-1/8$

In point-slope form: $y-17/4=-1/8(x-2)$

In slope-intercept form: $y=-1/8x+9/2$

What is the equation of the tangent line of f(x)=1/(2x)+4 f(x)=12x+4f(x)=1/(2x)+4 at x=2x=2x=2?