Consider the function f(x)=x^2e^(5x). For this function there are three important intervals: (−∞,A], [A,B], and [B,∞) where A and B are the critical numbers. Find A and B.
For each of the following intervals, tell whether f(x) is increasing (enter INC ) or decreasing (enter DEC ).
first we find derivative. Hereit is 2xe^(5x)+5x^2e^(5x) Easy to see that there two zeros x=0 and x=-2/5 so A=-2/5 and B=0. to see inc and dec regions we have just to check value of derivative. If it is positive at certain region then we have inc, if negative - dec. Hence (−∞,A]:inc[A,B]:dec [B,∞):inc