# Finding the maximum value on a restricted interval

Posted 2 years ago
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 Hi,I have the following function that I'm trying to maximize with respect to tau, but tau should be in a certain interval. And I know that I'm missing something, but can not find what as when I run my code I do not obtain anything. Maybe I'm using the wrong function, but even with Maxvalue I had the same issue. Any advice would be welcome,Best,Xavier Koch Attachments:
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Posted 2 years ago
 Beware that if you write $Assumptions = a > 0$Assumptions = \[Beta] > 0 the second line overrides the first one. It seems that your assumptions are not compatible with the constraint you impose on the variable \[Tau].
Posted 2 years ago
 Thanks for your reply, how should I write the assumptions then if this method is not efficient? Also, I don't see how the constraints could not match as they are just limiting the maximum value [Tau] can take.
Posted 2 years ago
 I've noticed that the original file is from an advanced version and not everyone can open it so here's a better version. Attachments:
Posted 2 years ago
 To make more than one assumption I would use And: $Assumptions = And[a > 0, \[Beta] > 0, d > 0, 1 > b > 0, c > 0, a > \[Tau]*\[Theta]A, \[Tau] > 0, \[Theta]A > \[Theta]B > \[Theta]C, a > \[Tau]*\[Theta]B, a > \[Tau]*\[Theta]C, Fb > 0, Fc > 0, 1 > \[Alpha] > 0] Your constraint is then myConstraint = Simplify[\[Tau] < 1/(2 (-\[Theta]A^2 + \[Theta]B^2))* (-2 a \[Theta]A + 2 a \[Theta]B - Sqrt[((2 a \[Theta]A - 2 a \[Theta]B)^2 - 4 (-\[Theta]A^2 + \[Theta]B^2)* (-((a^2 \[Theta]A)/(\[Theta]A + \[Theta]B)) - ( a^2 \[Beta] \[Theta]A)/(\[Theta]A + \[Theta]B) + ( a^2 p \[Beta] \[Theta]A)/(\[Theta]A + \[Theta]B) - ( a^2 p \[Alpha] \[Beta] \[Theta]A)/(\[Theta]A + \[Theta]B) \ + (a^2 \[Theta]B)/(\[Theta]A + \[Theta]B) + (a^2 \[Beta] \[Theta]B)/(\[Theta]A + \[Theta]B) - ( a^2 p \[Beta] \[Theta]B)/(\[Theta]A + \[Theta]B) + ( a^2 p \[Alpha] \[Beta] \[Theta]B)/(\[Theta]A + \ \[Theta]B)))])] I retract what I said about incompatibility: I had miswritten a symbol. Your constraint is indeed an interval, but its endpoints have different expressions, depending on the parameters: intrvl =Reduce[myConstraint &&$Assumptions, \[Tau], Reals] To maximize a parametric expression, FindMaxValue is not suitable, because it uses numerical methods. MaxValue can handle symbolic expressions: fnct = -((d (a - \[Theta]A \[Tau])^2)/(2 (b + c)^2)) + ( b (1 + \[Beta]) (a - \[Theta]A \[Tau])^2)/(8 (b + c)^2) + ((1 + \[Beta]) (a - \[Theta]A \[Tau])^2)/(4 (b + c)); MaxValue[{fnct, intrvl}, \[Tau]]// Simplify The interpretation of the symbolic result is tricky.