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Question: A question of plot and perhaps fsolve.

Question:A question of plot and perhaps fsolve.

Al86 145 Maple 2019
plot rootfinding
April 12 2020
0

Can someone help me with the following question?

 

I would like to plot the function f(x)=a*x*(1-x)+x*ln(x)+(1-x)ln(1-x) in the interval [x1,x2], where x1 and x2 are points that satisfy the following: df/dx(x=x1)=df/dx(x=x2)=0 and f(x1)=f(x2), where a is some parameter that is greater than 0.

I guess I need to use here fsolve, but I am not sure how.
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