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Answer to Question #17682 in Calculus for hsd

Question #17682
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 ).

Expert's answer
first we find derivative. Hereit is
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

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