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Showing that a Parabola's y values are greater than or equal to a line's y values

  1. Dec 12, 2016 #1
    1. The problem statement, all variables and given/known data
    the two functions [tex]f(x) = 5(√(x^2 +1))[/tex] [tex]g(x) = 3x + 4 [/tex].


    2. Relevant equations


    3. The attempt at a solution
    I can get the minimum point of f(x) and it is bigger than g(x) and that point, however g(x) is tangential to the curve f(x) at point 3/4.
    what else do i miss to show that f(x) is bigger or equal than g(x) for all x in R?
     
  2. jcsd
  3. Dec 12, 2016 #2

    Ray Vickson

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    Find the minimum of the difference function ##f(x) - g(x) = 5 \sqrt{x^2+1} -(3x+4)##.

    BTW: the word is parabola, not parabula; and anyway, you do not have a parabola anywhere in this problem.
     
  4. Dec 12, 2016 #3
    thanks

    its point 3/4. and it is the absolute minimum of the graph that's equal to 0, therefore f(x) >= g(x).
     
  5. Dec 13, 2016 #4

    Ray Vickson

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    Right!
     
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