Fit points and specify the slope at one of the points

Hello,

I have a series of 4 points:

x=[-0.385444	0	0.985035	4.36849];
y=[0.599583870363438	0.103	1.00644809697272	2.02362891855202];

At x=0.985035, I need the slope to be 0.

How do I do this?

I am familiar with the spline function, but it will only let me specify the slope at the begining and end of the curve.

Thank you.

[darova]

Can you make a drawing of ho the curve should look like

Answer 1

[Alex Sha]

Hi, try the function below:

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

to ensure the slope being 0 in point of "x=0.985035", should add a constraint of "p2*(2*xx)-p3*(exp(p4*xx)*p4)=0", where xx=0.985035. The result will be:

Root of Mean Square Error (RMSE): 0.287966090994206
Sum of Squared Residual: 0.331697878249934
Correlation Coef. (R): 0.913088032059037
R-Square: 0.833729754289445
Constrained Functions: p2*1.97007-p3*(exp(p4*0.985035)*p4)-0 = 1.44750877950628E-11

Parameter	Best Estimate
----------	-------------
p1	-0.154217819730129
p2	-0.391394281530186
p3	-0.727826672642068
p4	0.591562409273376