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Math Help - Find max and min for function

  1. #1
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    Find max and min for function

    f(x)=e^{x^2-2x} for 0<= x <=2
    (dont know how to insert less than or equal to)
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  2. #2
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    Quote Originally Posted by Minino777 View Post
    f(x)=e^{x^2-2x} for 0<= x <=2

    \frac{df}{dx}=\left(e^{x^2-2x}\right)(2x-2). Set to 0 to find critical points. Also don't forget to check the boundaries, x=0 and x=2.


    Quote Originally Posted by Minino777 View Post
    (dont know how to insert less than or equal to)
    In LaTeX, use \le (or \leq)
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  3. #3
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    critical points

    I only get one critical point x=1 within the boundaries, right?
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    Quote Originally Posted by Minino777 View Post
    I only get one critical point x=1 within the boundaries, right?
    Yup, and that is also the only critical point within the domain of the function (all reals).
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  5. #5
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    Quote Originally Posted by Minino777 View Post
    I only get one critical point x=1 within the boundaries, right?
    Yes, but you should also look at the endpoints of the interval as well. This gives you 3 points to look at.

    To find the minimum and maximum, evaluate the function at all 3 of those points and see which is the smallest and which is the largest.
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    Quote Originally Posted by drumist View Post
    Yes, but you should also look at the endpoints of the interval as well. This gives you 3 points to look at.

    To find the minimum and maximum, evaluate the function at all 3 of those points and see which is the smallest and which is the largest.
    This was already mentioned..?
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