Wanna find x that maximize a function including symbolic variables

Hello,

I wanna find x that maximize the following unction including symbolic variables. Please teach me how to do so.

K,m,T,D >0

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syms K,m,T,D,x
f(x)=sqrt(1/( (K-(m+T*D)*x^2)^2 + x^2*(D+T*K-T*m*x^2)^2))

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Best regards

[Torsten]

Set the denominator to zero and use Matlab's "solve" to solve for x^2.

If you don't get x real-valued, differentiate the denominator with respect to x, set the derivative to zero and again use Matlab's "solve" to solve for x.

[嵩人 藤森]

thx!!!

Answer 1

[KSSV]

syms K m T D x
f(x)=sqrt(1/( (K-(m+T*D)*x^2)^2 + x^2*(D+T*K-T*m*x^2)^2)) ;
df = diff(f,x)

df(x) = 

s = solve(df,x)

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

s = 

[嵩人 藤森]

thx, you helped me a lot