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.
A=
B=
For each of the following intervals, tell whether f(x) is increasing (enter INC ) or decreasing (enter DEC ).
(−∞,A]:
[A,B]:
[B,∞)

Expert's answer

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

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

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