F(s) = s + 2/s + 10. To find the maximum value of F(s) in the interval [1,4], we differentiate F(s) and equate the derivative to 0. Also, at the point of maximum value F''(s) is negative.

F(s) = s + 2/s + 10

F'(s) = 1 - 2/s^2

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F(s) = s + 2/s + 10. To find the maximum value of F(s) in the interval [1,4], we differentiate F(s) and equate the derivative to 0. Also, at the point of maximum value F''(s) is negative.

F(s) = s + 2/s + 10

F'(s) = 1 - 2/s^2

1 - 2/s^2 = 0

=> s^2 - 2 = 0

=> s = +sqrt 2 and s = -sqrt 2

But F''(s) = 6/s^3 which is positive, therefore there is no maximum value for F(s).

**The required maximum value of F(s) does not exist.**