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Fundamental Theorem of Calculus

  1. May 16, 2012 #1
    1. The problem statement, all variables and given/known data

    F(x) = ∫ cos (1+t^2)^-1) from 0 to 2x - x^2

    Determine whether F has maximum or minimum value

    2. Relevant equations



    3. The attempt at a solution
    I tried finding
    F'(x) = Dx (∫ cos (1+t^2)^-1) from 0 to 2x - x^2)
    = (2-2x)cos[(1+(2x-x^2))^-1]

    What do I do next? equate F'(x) = 0 and find F''(x) ?

    Please help. Thank you.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 16, 2012 #2

    chiro

    User Avatar
    Science Advisor

    Hey inter060708 and welcome to the forums.

    Turning points happen when the derivative is zero, and the second-derivative (unless it's an inflexion point) will determine whether something is a minimum of maximum based on the sign.

    Remember that the second derivative says how fast the derivative is changing, so if it is negative then it means you have a maximum and if it's positive it means a minimum since the derivative (which is the rate of change) will be either 'going negative' or 'going positive'.

    So the first thing you need to do is find F'(x) = 0 and take it from there.
     
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