How can i find the co-ordinates of a point where the slop is -1 in below graph ?

Here is a set of all the points known for the graph. Now how how can i find at which point(s) the slope of the curve is (-1) ?

[John D'Errico]

Huh? A line with a slope of 90 degrees is not a line with a slope of -1. 90 degrees would imply what we usually call an infinite slope, but really, a slope larger than any finite number.

Anyway, there are THREE columns of numbers in that file, though the first column just appears to be a row number. But it was still labeled as vin. So what slope would you be hoping to compute?

Answer 1

[Star Strider]

Try this —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1285050/cmos.txt', 'VariableNamingRule','preserve')

T1 = 181×3 table
    vin     V(vin)    V(vout)
    ____    ______    _______

       0        0       1.8  
    0.01     0.01       1.8  
    0.02     0.02       1.8  
    0.03     0.03       1.8  
    0.04     0.04       1.8  
    0.05     0.05       1.8  
    0.06     0.06       1.8  
    0.07     0.07       1.8  
    0.08     0.08       1.8  
    0.09     0.09       1.8  
     0.1      0.1       1.8  
    0.11     0.11       1.8  
    0.12     0.12       1.8  
    0.13     0.13       1.8  
    0.14     0.14       1.8  
    0.15     0.15       1.8  

Vin = T1.('V(vin)');
Vout = T1.('V(vout)');

dVoutdVin = gradient(Vout) ./ gradient(Vin);
[minslope,idx] = min(dVoutdVin)

minslope = -26.7229

idx = 79

idxv = find(diff(sign(dVoutdVin + 1)));
% idxv = [1 idx numel(Vin)];
for k = 1:numel(idxv)
    idxrng = idxv(k)-1 : idxv(k)+1;
    xv(k,:) = interp1(dVoutdVin(idxrng), Vin(idxrng), -1);
    yv(k,:) = interp1(Vin(idxrng), Vout(idxrng), xv(k));
end

Slope_Negative_1_Coordinates = table(xv, yv)

Slope_Negative_1_Coordinates = 2×2 table
      xv         yv   
    _______    _______

    0.60843     1.7097
    0.86692    0.11947

figure
yyaxis left
plot(Vin, Vout, 'DisplayName','Data')
hold on
plot(xv, yv, 'rs', 'DisplayName','Slope = -1')
hold off
xlabel('$V_{in}$', 'Interpreter','latex')
ylabel('$V_{0ut}$', 'Interpreter','latex')
yyaxis right
plot(Vin, dVoutdVin, 'DisplayName','Derivative')
ylabel('$\frac{dVout}{dVin}$', 'Interpreter','latex')
grid
legend('Location','best')

EDIT — (5 Feb 2023 at 14:33)

Added ‘Slope_Negative_1_Coordinates’ table.

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