Let F(s) = s+2/s+10. Find the maximum of F(s) on the interval [1,4].

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.