MATLAB: FInd maximum in cubic spline interpolant

maximumspline interpolant

I got a set of data, x and y
I was trying to find an eqaution that bu basic fitting and it comes out that spline interpolant is the best one to fit in. (quad and cubic has a peak lower than actual value, so i can not use them)
Now, I want an actual equation that represents a line between two point.
Also I want to find a maximum y-value in a line of cubic spline interpolant, not from the actual data.
I tried findpeak, but it display the y-vale from my data.
So is there a way to do it??
x =
    0.7000
    0.7500
    0.8000
    0.8500
    0.9000
    0.9500
    1.0000
    1.0500
    1.1000
    1.1500
    1.2000
    1.2500
    1.3000
y =
1.0e+003 *
    1.8367
    1.9180
    1.9953
    2.0677
    2.1333
    2.1883
    2.2251
    2.2318
    2.2097
    2.1746
    2.1356
    2.0958
    2.0562
plot (x,y)
using basic fit tool, clicked on a spline interpolant
and got stuck from here
Cheers,

Best Answer

EDIT
new data
x = [0.70000
   0.75000
   0.80000
   0.85000
   0.90000
   0.95000
   1.00000
   1.05000
   1.10000
   1.15000
   1.20000
   1.25000
   1.30000];
y = [1836.7
   1918.0
   1995.3
   2067.7
   2133.3
   2188.3
   2225.1
   2231.8
   2209.7
   2174.6
   2135.6
   2095.8
   2056.2];
for MATLAB R2013a and later
[~,ii] = findpeaks(y);
F = griddedInterpolant(x,y,'spline');
xmaxs = arrayfun(@(xx)fminsearch(@(x)-F(x),xx),x(ii));
x1 = linspace(x(1),x(end),100);
plot(x,y,'go',x1,F(x1),'b-',xmaxs,F(xmaxs),'r+');
for older releases MATLAB
[~,ii] = findpeaks(y);
F = interp1(x,y,'spline','pp');
xmaxs = arrayfun(@(xx)fminsearch(@(x)-ppval(F,x),xx),x(ii));
x1 = linspace(x(1),x(end),100);
plot(x,y,'go',x1,ppval(F,x1),'b-',xmaxs,ppval(F,xmaxs),'r+');
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