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Math Help - Maximum and Minimum

  1. #1
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    Maximum and Minimum

    Find the largest and smallest values taken on by the function on the interval 0 < X < 2


    I understand the procedure, finding the crit points first in which i got x = 1 for the real values.

    Max = 1.66637 Correct to 4 significant figures.
    Min = ?

    I cant seem to get the minimum value though please help!
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  2. #2
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    Re: Maximum and Minimum

    Hey fourhire.

    Hint: What did you obtain for the first derivatives of this function?
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  3. #3
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    Re: Maximum and Minimum

    hey Chiro, f ' (x) = exp(x-1)^2 5cos(5x) + 2sin(5x)exp(x-1)^2(x-1)
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  4. #4
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    Re: Maximum and Minimum

    Now you have to find when that equals zero and then do a second derivative test to see where the minimum lies.
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  5. #5
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    Re: Maximum and Minimum

    Hi Chiro, so to clarify, f'(x)= 0 gives you maximum? and f''(x)=0 gives you minima?
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  6. #6
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    Re: Maximum and Minimum

    f'(x) = 0 helps you find the turning points which can be either a minimum, maximum, or point of inflexion.

    Then for this particular x (or x's) that satisfy f'(x) = 0, the minimum satisfies f''(x) > 0, the maximum f''(x) < 0 and the point of inflexion satisfies f''(x) = 0 for the particular turning point for that particular x.
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