Do NOT find an
function. That would be tedious and unnecessary work.
This is another way of wording a very familiar problem:
and a point on , find the tangent line to at and use it to estimate the value of .'
Split the absolute value into a piecewise function and differentiate.
Or, you could recall a special note about the antiderivative of
: While you can generally leave it as , it actually equals .
Use concavity to determine if your answer to part (a) is an under or over estimate of the actual value of
. Justify your answer.
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.