# Finding the point of inflection on a curve

Asked by Wern-Juin Choy on 2 Jan 2012
Latest activity Answered by Teja Muppirala on 4 Jan 2012

Hi everyone, I have a question.

Is there any code that allows one to find the point of inflection on a step response curve of a transfer function? An example is given below.

```Ts = 0.0005;
```
```%Continuous system
Ps = tf(2,[1,12,20.02]);
Pz = c2d(Ps,Ts,'zoh');
```
```%response
figure(1)
hold on
step(Pz)
hold off
```

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Answer by Teja Muppirala on 4 Jan 2012

You need to find where the 2nd derivative is zero. There are many different ways to approach this. This is one possible way:

```Ts = 0.0005;
%Continuous system
Ps = tf(2,[1,12,20.02]);
Pz = c2d(Ps,Ts,'zoh');
%response
[y,t] = step(Pz);
```
```plot(t,y);
hold on;
```
```% Estimate the 2nd deriv. by finite differences
ypp = diff(y,2);
```
```% Find the root using FZERO
t_infl = fzero(@(T) interp1(t(2:end-1),ypp,T,'linear','extrap'),0)
y_infl = interp1(t,y,t_infl,'linear')
```
```plot(t_infl,y_infl,'ro');
```

Another way would be to find the roots of the step response of

```tf([2 0 0],[1,12,20.02]);
```