Question

How to find critical points, intervals of increasing and decreasing, local minimums and maximums, intervals of concavity up/down, and inflection points?

Answer 1

Critical points occur when the 1st derivative equals zero or doesnt exist.
Inflection points can occur when the 2nd derivative equals zero or doesnt exist, but for is to be an inflection point, the 2nd derivative must change sign at that point.

Answer 2

If the 2nd derivative is positive then it is concave up over an interval.
If the 2nd derivative is negative then it is concave down over an interval.

Answer 3

Decreasing if the 1st derivative is negative.
Increasing if the 1st derivative is positive.

Answer 4

So for the critical point I find the derivative and set it equal to zero and solve?

Answer 5

Local max can occur at critical points. Local min can occur at critical points. Find the critical points of a function, then do a 1st derivative test (number line analysis) or evaluate your critical points and endpoints on the original function to determine the local max and local min.

Answer 6

Yes, for critical points, find the 1st derivative. Find where it equals 0 and/or does not exist.

Answer 7

can you explain the intervals of increasing and decreasing more clearly?

Answer 8

Are the local max's ONLY the critical points?

Answer 9

Umm, critical points can be local max's or min's.

Answer 10

I'll draw and solve a problem , so you can see what I mean for the intervals of increase and decrease..ok?

Answer 11

okay