# How to find the positive maximum value of a function

• Keysa

#### Keysa

TL;DR Summary
I want to find the positive maximum value of a function, but so far I always ended up with either a negative value or the value doesn't even show up.
This is the code that i wrote

Clear["Global*"]
Z = 500;
W = 100000;
G = 250;
H = 100;
K = 0.5;
T = 30;
L = 4000;
P = 5;
S = 2.5;
Y = 1;
A = 0.1;
V = 2.5;
J = 8000;
f[x_] := 1/
x {(J*Z*x*(2*Y - x))/(
2*Y) - ((W + T*G) + ((L + T*P)*2*Z*Y*(1 - ((Y - x)/Y)^1.5))/
3 + (H + T*S + A*L)*((
2*Z*Y*2*Y - 2*Z*Y*2*Y*((Y - x)/Y)^2.5 -
2*Z*Y*5*x*((Y - x)/Y)^1.5)/15))};
Plot[f[x], {x, -2, 2}]
FindMaximum[f[x], x]

Hay Keysa, what function and what domain? Can you write it in LaTeX? You use Python?

Hello Keysa,

It would help if you mentioned the language in which you try to do this.
If I use Excel () to plot your function, I get

and an error if ##x\ge 1##.

You sure you have no typos in your very long expression ?

##\ ##

Some formatting and added parenthesis would help us to see what your equation is. I can't see how much is in the denominator. If @BvU's graph is correct, then the maximum depends on the range of x.

What I plotted is
Code:
f(x) = 1/x *((J*Z*x*(2*Y - x))/(2*Y) - ((W + T*G) + ((L + T*P)*2*Z*Y*(1 - ((Y - x)/Y)^1.5))/3 + (H + T*S + A*L)*((2*Z*Y*2*Y - 2*Z*Y*2*Y*((Y - x)/Y)^2.5 -2*Z*Y*5*x*((Y - x)/Y)^1.5)/15)))`

but, since I am not a computer nor a robot, I have a hard time chopping it up into digestable pieces.
Do you have a source, an original, or anything that helps sorting out your function ?

##\ ##