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A Find the minimum without Calculus or Graphing

  1. Nov 16, 2015 #1
    • Poster is on a 10-day vacation from the PF for repeatedly misplacing schoolwork type questions
    ƒ(ß)=.5sec(ß) + √[1+(sec2(ß)/4)+tan(ß)/√(2)]
    Without graphing it or using calculus find the minimum. I already know the answer but want to know how to do it. It s at π/12 and is something like 1.5.
    First off this is NOT a homework problem. I already know the answer is something like 1.5 at π/12 but I want to know how to do it. DONT PUT THIS IN A HOMEWORK SECTION.
     
  2. jcsd
  3. Nov 17, 2015 #2
    Perhaps one can use trig identities to simplify it first.
     
  4. Nov 17, 2015 #3

    BvU

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    I'd like to know the actual function. Probably not
    or, as we write it here $$ {1\over 2\cos\beta}+ \sqrt{ 1 + {1\over 4 \cos^2\beta} + {1\over \sqrt 2}\tan\beta} $$ surely ?
     
  5. Nov 17, 2015 #4
    Probably not.
    f(Pi/12)=1.73
    f(0)=1.62

    @OP
    Have you checked if the Pi/12 and 1.5 satisfy the expression?
     
  6. Nov 17, 2015 #5
    Make a large table of values at small step size.

    Pick the three lowest adjacent values.

    Fit to a quadratic.

    Use the standard formula for the minimum of a parabola opening upward.
     
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