I am working with a curve with two parameters (α,β), in addition to the independent (x between 0 and 1) and dependent (y) variables. I have a function which takes a value for the independent variable and the two parameters `function(x,α,β)`

and returns the slope and y-intercept (`[m,b]`

) for the tangent of the curve at the given x.

I need to find values of x with the same tangent line, i.e. `[m,b]`

for `x[0]`

= `[m,b]`

for `x[n]`

. Is there a solver I can use for this?

For reference/experimentation, here is the function:

```
def tan_Gmix_van_Laar(x,α,β):
if x>1 or x<0:
print("for tan_Gmix_van_Laar: x out of bounds")
return
G = (x-x**2)*α*β/(β+(α-β)*x) + x*np.log(x)+(1-x)*np.log(1-x)
m = α*β/(β+(α-β)*x)*(1-2*x) - α*β*(α-β)/((α-β)*x+β)**2*(x-x**2) + np.log(x/(1-x))
b = G-m*x
tanparams = np.array([m,b])
return tanparams
```

`alpha`

and`beta`

there instead. Or`a`

and`b`

if you don't like the length. – Grismar Mar 27 at 0:00