Do NOT find an f(x) function. That would be tedious and unnecessary work.
This is another way of wording a very familiar problem:
'Given f '(x) and a point on f(x), find the tangent line to f(x) at x = −3 and use it to estimate the value of f(−3.1).'
Split the absolute value into a piecewise function and differentiate.
Or, you could recall a special note about the antiderivative of x−1: While you can generally leave it as ln(x), it actually equals ln|x|.
If a function is concave down, all tangent lines will be above the curve.
If a function is concave up, all tangent lines will be below the curve. Sketch this to verify.