### Home > APCALC > Chapter 8 > Lesson 8.2.3 > Problem 8-88

Let * *is shown at right.

Evaluate

and.Is

? Consider the symmetry of

betweenand.Express

in terms of .What is

? What is?Is

differentiable over the interval? Explain. Points of NON-differentiability include cusps, endpoints, jumps, holes, and vertical tangents.

Determine all values of

in the intervalwhere has a relative maximum.Recall that a local maximum exists where the derivative changes from positive to negative. This can happen where

or where.Notice that

; after all, the derivative of an integral is the original function.Write the equation of the line tangent to

at.What is the slope of

at(see second hint in part (e))? What is the-value?Determine all values of

in the intervalwhere has a point of inflection.Concavity is the slope of the slope. So inflection points are where the slope of the slope changes.