This question will walk you all the way through find the local extrema of a function, and along the way finding the increasing/decreasing intervals. Consider the function f(x)=x48x2+3

Now, again we can test ANY point in each subinterval to determine the concavity of the entire subinterval. Choose ANY number in the left-most interval: When plugged into f''(x) (the second derivative), we get a Select an answer negative positive value, hence the entire left-most interval is Select an answer Concave Up Concave Down Choose ANY number in the middle interval: When plugged into f''(x) (the second derivative), we get a Select an answer positive negative value, hence the entire middle interval is Select an answer Concave Up Concave Down Choose ANY number in the right-most interval: When plugged into f''(x) (the second derivative), we get a Select an answer positive negative value, hence the entire right-most interval is Select an answer Concave Down Concave Up Finally, the function f(x)f(x) is Concave Up on the interval[s]: Concave Down on the interval[s]: Also, note that both potential inflection points ARE inflection points since the concavity changes at both.