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

1 Answer
Apr 3, 2018

#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.