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

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

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Answer 1 · 2018-04-03T14:36:05

$y = - \frac{x}{16} + \frac{1}{2}$ $y=-x/16+1/2$

Explanation:

We need to differentiate $\frac{1}{x}$ $1/x$ using the general power rule to find the slope/ gradient of the tangent line.

$\frac{d}{d x} [x^{n}]$ $d/dx [x^n]$ = $\frac{n x^{n - 1}}{n - 1}$ $[nx^[n-1]]/[n-1]$ ..... so $\frac{d}{d x} \frac{1}{x}$ $d/dx 1/x$ = $\frac{d}{d x} [x^{- 1}]$ $d/dx[x^-1]$ = $[- x^{- 2}]$ $[-x^-2]$ = $- \frac{1}{x^{2}}$ $-1/x^2$ ...... $[1]$ $[1]$

When $x = 4$ $x=4$ , substituting in ..... $[1]$ $[1]$ , slope = $- \frac{1}{16}$ $-1/16$

From $y = \frac{1}{x}$ $y=1/[x]$ , when $x = 4$ $x=4$ , $y = \frac{1}{4}$ $y=1/4$

Therefore the equation of the tangent line= $y - \frac{1}{4} = - \frac{1}{16} [x - 4]$ $y-1/4=-1/16[x-4]$
and when evaluated will give the above answer.

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

1 Answer

Explanation:

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