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

Let

*g*(*x*) =where *f*is shown at right. Homework Help ✎Find

*g*(2) and*g*(4).Is

*g*(−2) =? Express

in terms of *g*.Is

*g*differentiable over the interval −2 <*x*< 6 ? Explain.Find all values of

*x*on the interval −2 <*x*< 6 where*g*has a relative maximum.Find the line tangent to

*g*at*x*= 4.Find all values of

*x*on the interval −2 <*x*< 6 where*g*has a point of inflection.

Consider the symmetry of the *f*(*t*) between *t* = −2 and *t* = 2.

What is *k*? What is *a*?

Points of NON-differentiablity include cusps, endpoints, jumps, holes and vertical tangents.

Recall that a local maximum exists where the derivative changes from positive to negative. This could happen where *f* '(*x*) = 0 or where *f* '(*x*) = DNE.

Notice that *g*'(*x*) = *f*(*x*); after all, the derivative of an integral is the original function.

What is the slope of *g*(*x*) at *x* = 4 (see second hint in part (e))? What is the *y*-value?

Concavity is the slope of the slope. So inflection points are where the slope of the slope changes.