# Define a function and plot its min

**URL:** <https://community.freefem.org/t/define-a-function-and-plot-its-min/793>\
**Category:** General Discussion\
**Created:** [February 10, 2021, 4:50pm UTC](https://community.freefem.org/t/define-a-function-and-plot-its-min/793 "2021-02-10T16:50:24Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Aicha](https://avatars.discourse-cdn.com/v4/letter/a/ec9cab/32.png) [@Aicha](https://community.freefem.org/u/Aicha)\
**Post date:** [February 10, 2021, 4:50pm UTC](https://community.freefem.org/t/define-a-function-and-plot-its-min/793/1 "2021-02-10T16:50:24Z")

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Hi,  
i want to plot with FF++, the following function  
min\_{mu \> 0} (D \* mu^3 \* exp(mu \* tau)}{(mu+sigma)\*exp(mu \* tau)-a \* b \* w0)

the data are: real tau=1, w0=1.0, sigma=1.0, D=0.001, a=0, b=2

then i try to do this:

real tau=1.0;  
real w0=1.0;  
real sigma=1.0;  
real D=0.001;  
real a=0.0;  
real b=2.0;

func real F (real mu)  
{  
return (D \* mu^3 \* exp(mu \* tau))/( (mu+sigma2) \* exp(mu \* tau)-a \* b \* w0);  
};  
func real F (real mu)=  
{  
return (D \* mu^3 \* exp(mu \* tau))/( (mu+sigma2) \* exp(mu \* tau)-a \* b \* w0);  
};  
Vh Fh=F;

I have to plot minimum of F for mu \> 0 (dont for all real mu). So how we define this minum?

Thank’s in advanced