CPM Homework Banner
7-50.

Use the first and second derivatives to determine the following locations for . Homework Help ✎

  1. Relative minima and maxima

    Remember: Finding where or DNE will identify CANDIDATES for minima and maxima.
    You need to complete the 1st or 2nd Derivative Test to confirm which is which.

  2. Intervals over which f is increasing and decreasing

    When is positive, then has positive slopes, which means is increasing.

  3. Inflection points

    Remember: Finding where or = DNE will identify CANDIDATES for inflection points.
    You need to do further investigation to determine if it is (or is not) an inflection point.

    Either test for a sign change of before and after the candidate point. Or evaluate at the candidate.
    If ≠ 0, then it is a point of inflection.

  4. Intervals over which f is concave up and concave down

    When is positive, then has positive slopes, which means  is concave up.