Question

What is the equation of the tangent line of `f(x)=1/absx` at `x=4`?

Answer 1

`y=-x/16+1/2`

Explanation:

We need to differentiate `1/x` using the general power rule to find the slope/ gradient of the tangent line.

`d/dx [x^n]`= `[nx^[n-1]]/[n-1]`..... so `d/dx 1/x`=`d/dx[x^-1]`=`[-x^-2]` = `-1/x^2`......`[1]`

When `x=4`, substituting in .....`[1]`, slope =`-1/16`

From `y=1/[x]`, when `x=4`, `y=1/4`

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

Hope this was helpful.