RootOf interpretation

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Question:RootOf interpretation

Posted: Harry Garst 239 Product: Maple

March 11 2021

I was hoping to find a nice symbolic solution for the root of this equation:

a,c,d,k are parameters.
Unfortunately, I got an RootOf expression, which does not make sense to me. Assumptions do no help me further.

Next week, I have to present my results, but I don't know how to interpret is (the help file does not bring any relief). Is there something to say about the root? Suppose, I wanted to use side restriction on a problem? E.g., find a solution conditional on the fact that the derivative is zero.

Clearly, in the plot it seems simple.

In one case there is a solution Maple provides: a (a parameter)

This seems strange, because numerically there is one solution (and clearly not a).

User Interface: 1502365
Kernel: 1502365
Library: 1502365

(1)

f := proc (t) options operator, arrow; c/(1+exp(k*(t-a)))-c*(t-a)*k*exp(k*(t-a))/(1+exp(k*(t-a)))^2+d/(1+exp(-k*(t-a)))+d*(t-a)*k*exp(-k*(t-a))/(1+exp(-k*(t-a)))^2 end proc

proc (t) options operator, arrow; c/(1+exp(k*(t-a)))-c*(t-a)*k*exp(k*(t-a))/(1+exp(k*(t-a)))^2+d/(1+exp(-k*(t-a)))+d*(t-a)*k*exp(-k*(t-a))/(1+exp(-k*(t-a)))^2 end proc

(2)

Originally a, renamed a~:
  is assumed to be: RealRange(Open(0),infinity)

Originally k, renamed k~:
  is assumed to be: RealRange(Open(0),infinity)

Originally t, renamed t~:
  is assumed to be: RealRange(Open(0),Open(21))

(3)

Warning, solve may be ignoring assumptions on the input variables.

(k*a+RootOf(-(exp(_Z))^4*d+(exp(_Z))^3*_Z*c-(exp(_Z))^3*_Z*d-(exp(_Z))^3*c-3*(exp(_Z))^3*d+2*c*_Z*(exp(_Z))^2-2*(exp(_Z))^2*_Z*d-3*c*(exp(_Z))^2-3*d*(exp(_Z))^2+c*_Z*exp(_Z)-d*_Z*exp(_Z)-3*c*exp(_Z)-d*exp(_Z)-c))/k