continuity of a fit function in different regions

I have probelm in continuity of a fitting of a function where I divided it to two regions the first region is linear and second one is quadratic where I'm using lsqcurvefit for fitting

Answer 1

[Alex Sha]

Attach your data file please.

Answer 2

[mohammad hadi]

you can find the data in the attchment and I want to have the derivative of the function at x=1 to be zero.

thank you

Answer 3

[Alex Sha]

Hi, the function below meets your requirements， with the derivative to be zero at x=1

y = p1+p2*(((x-p3)*(x+p4))^2)^p5;

Root of Mean Square Error (RMSE): 0.111454525338652
Sum of Squared Residual: 0.236020113150822
Correlation Coef. (R): 0.999608307854672
R-Square: 0.999216769132081
Adjusted R-Square: 0.999118865273591
Determination Coef. (DC): 0.999216769132081
Chi-Square: 0.322625091206584
F-Statistic: 4465.16963433769
Constrained Functions: p2*((p5*((((1-p3)*(1+p4))^2)^(p5-1)))*((2*((1-p3)*(1+p4)))*(1+p4+1-p3)))-0 = 0

Parameter	Best Estimate
----------	-------------
p1	12.2679122419038
p2	-12.1133796289348
p3	1.00000000000003
p4	-0.999999999999971
p5	0.321345944716431