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In the attached file (Minimising) I minimise the following function
by differentiating w.r.t PLu, solving for PLu and then substituting back into the original function.
I do this in two ways
First: I provide values for Pv, T and Pu, differentiate and then use fsolve and a single value is returned for PLu. I then substitute this Plu value and the same Pv, T and Pu values into the function to get the minimum value at the specified Pv, T and Pu.
Second: I differentiate without providing values for Pv,T and Pu and then use solve but I get two solutions.
If I substitute each solution back into the original function and then provide values for Pv, T and Pu, one solution provides the minimum value and the other does not.
Which solution provides a minimum value seems to vary depending on the values of Pv, T and Pu.
Why does Maple find 2 solutions and why do they seem to vary as to which one provides a minumum?