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General
Easy

Question

Let f left parenthesis x right parenthesis equals not stretchy integral e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis d x. Then f decreases in the interval :

  1. (−infinity, −2)    
  2. (−2, −1)    
  3. (1, 2)    
  4. (2, infinity)    

The correct answer is: (1, 2)


    f ´ left parenthesis x right parenthesis equals e to the power of x end exponent left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis
    f ´ left parenthesis x right parenthesis less than 0when 1 < x < 2
    f(x) decreases in the interval (1, 2).

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