### Home > APCALC > Chapter 7 > Lesson 7.1.5 > Problem 7-52

Let

Estimate

.Do NOT find an

function. That would be tedious and unnecessary work.This is another way of wording a very familiar problem:

'Givenand a point on, find the tangent line toatand use it to estimate the value of.'Find

?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 ln| *x*|.Use concavity to determine if your answer to part (a) is an underestimate or an overestimate 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.