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Math Help - Find the intervals and extreme values

  1. #1
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    Post Find the intervals and extreme values

    Here's the question:

    Function (X+2) e^ -3X. Find intervals where it is increasing and decreasing. Find the extreme values and indicate the max or min.

    Here is my best attempt at this problem:
    Y= (X+2) e^ -3X
    Y' = (e^-3X) + (X+2) ((e^-3x)(-3)

    Y' = (e^-3X) (1+ (-3(X+2))
    Y' = (e^-3X) (1- 3X-6))
    Y' = -(e^-3X) (3X+5)

    Now I am stuck. I don't know what to do.
    The only thing I can think of is trying to find a value for X that would cause Y' = 0, but I haven't been able to do that.

    Can anyone help me?
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  2. #2
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    Assuming your algebra is correct then Y' =0 if e^{-3x} =0 or 3x + 5 =0

    e^{-3x} =0 has no solutions

    3x + 5 =0 implies x=-5/3
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  3. #3
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    Quote Originally Posted by SpringFan25 View Post
    Assuming your algebra is correct then Y' =0 if e^{-3x} =0 or 3x + 5 =0

    e^{-3x} =0 has no solutions

    3x + 5 =0 implies x=-5/3
    Thank you. I completely forgot about being able to do that...

    Y' = -(e^-3X) (3X+5)

    So when X > -5/3 then F'(X) increases, when X < -5/3 then F'(X) decreases.

    Therefore my final answer should be?:
    F(x) increase on (-5/3, +infinity) and decreases on (-infinity, -5/3)

    X = -5/3 is the local min.


    Am I missing anything else?
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