### Home > CALC > Chapter 8 > Lesson 8.2.3 > Problem 8-87

Let is shown at right.

Find

and.Since

was defined as , Is

? Consider the symmetry of the

betweenand.Express

in terms of .

What is? What is?Is

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

Find all values of

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

or whereDNE. Notice that

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

at.What is the slope of

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

on 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.