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Optimizing equation root symbolically gives no result

Posted 2 years ago

Hi how are things? Can someone tell me a software to find the minimum or maximum of this equation. It is a parameterized equation with a single variable x. In another word find the exact or approximate roots of this equation.

Copyable Plain Text:

-a b e^(-a x^b) x^(b - 1) + 1/8 (-a b e^(-a x^b) x^(b - 1) (1 - e^(-c(1 - x)^b)) - b c e^(-c(-x + 1)^b - a x^b) (-x + 1)^(b - 1))=0

Wolfram Language code:

-((a b x^(b - 1))/E^(a x^b)) + (1/8) (-((a b x^(b - 1) (1 - E^(-c[1 - x]^b)))/E^(a x^b)) - b c E^(-c[-x + 1]^b - a x^b) (-x + 1)^(b - 1))=0
4 Replies
Posted 2 years ago

Crossposted here.

POSTED BY: Rohit Namjoshi

Thank you very much for the reply. But actually what I want is the general expression with the parameters. Will it be able to isolate me x or find the root? hannn x is valid on this interval 0<x<1

For today's mathematics it is impossible to solve for the general expression with the parameters.

It's only possible for: b=1.

 b = 1; Solve[eq == 0, x]

(* {{x -> -(Log[(a E^-c - c E^-c)/(9 a)]/c)}} *)
POSTED BY: Mariusz Iwaniuk

Try:

ClearAll["`*"]; Remove["`*"];

eq = -((a b x^(b - 1))/E^(a x^b)) + (1/
      8) (-((a b x^(b - 1) (1 - E^(-c (1 - x)^b)))/E^(a x^b)) - 
      b c E^(-c (-x + 1)^b - a x^b) (-x + 1)^(b - 1));

a = 1;
b = 2; 
c = 3;

Maximize[eq, x]
% // N
NMaximize[eq, x]

Minimize[eq, x]
% // N
NMinimize[eq, x]
POSTED BY: Mariusz Iwaniuk
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