.

on

      454. on

      455. on

Finding Intervals of Increase and Decrease

       456–460 Find the intervals of increase and decrease, if any, for the given function.

      456.

      457. ,

      458. on

      459. on

      460. ln

Using the First Derivative Test to Find Local Maxima and Minima

       461– 465 Use the first derivative to find any local maxima and any local minima.

      461.

      462.

      463.

      464. on

465. on

Determining Concavity

       466– 470 Find the intervals where the given function is concave up and concave down, if any.

      466.

      467.

      468.

      469.

      470. on

Identifying Inflection Points

       471–475 Find the inflection points of the given function, if any.

      471.

      472.

      473. on

      474. on

      475.

Using the Second Derivative Test to Find Local Maxima and Minima

       476–480 Use the second derivative test to find the local maxima and local minima of the given function.

      476.

477.

      478.

      479.

      480. on

Applying Rolle’s Theorem

       481– 483 Verify that the function satisfies the hypotheses of Rolle’s theorem. Then find all values c in the given interval that satisfy the conclusion of Rolle’s theorem.

      481. ,

      482. , [–8, 0]

      483. ,

Using the Mean Value Theorem

       484–486 Verify that the given function satisfies the hypotheses of the mean value theorem. Then find all numbers c that satisfy the conclusion of the mean value theorem.

      484. ,

      485. ,

      486.