Find out the maxima or minima of the following function.

Question

f(x)=(x-2)6(x-3)5

Answer 1

As Philip P pointed out the function you posted is most likely (x-2)^6 * (x-3)^5. If this is the case, you will need to find the first derivative using the product and chain rules. If you post your results along with any insight you have I will be glad to help further. I encourage you to go past the point of finding the derivative if at all possible. -------- Just for the sake of closure I am going to post a general solution to this problem. Here is one way to solve this: 1. Find the first derivative of the function and set it = 0. The results (assuming there are any) are called critical points. ***Beware. Any points you find may or may not be local max or min (take f(x) = x3 for example). You must use other methods to determine max or min.*** 2. Evaluate critical points for max/min. There are a few ways to do this: Use the second derivative test. Take the second derivative of the function and set it = to zero. You can use these points to determine concavity, points of inflection, etc but I'm not going into that here because determining the second derivative of this function is a bear. Choose points on either side of critical points found and evaluate them and the critical points against the *original* f(x). Make sure to choose points that are not too far away, but also relatively easy to evaluate against f(x). If the points near the critical point are both greater than the critical point, the function curves up and the critical point is a minimum point. If the points are both less than the cp then it is a maximum point. If one is GT and one is LT, it is not a max or min point. (It could possibly be a point of inflection but I am not 100% sure it needs to be) In general, the second derivative test is preferred as it tends to reveal more about the behavior of the function. But in this case the question was to find local max/min and finding the second derivative was messy at best. Please let me know if you or anyone has any questions about what I wrote or takes issue with anything. Christian