Finding Slope of a curve at a specific point

How can i calculate the slope of the curve at the point presented in a red star.

Answer 1

[Star Strider]

Try something like this —

x = linspace(1, 10);
y = sin(2*pi*x/3) + cos(2*pi*x/9);

dydx = gradient(y) ./ gradient(x);

xv = rand*max(x)                                            % Choose A Random Point

xv = 4.1240

yv = interp1(x, y, xv)                                      % Interpolate 'y' Vector

yv = -0.2597

dydxv = interp1(x, dydx, xv)                                % Interpolate Derivative Vector

dydxv = -1.6437

figure
plot(x, y)
hold on
plot(xv, yv, '*r')
hold off
text(xv, yv, sprintf('  \\leftarrow Slope at (%.3f, %.3f) = %.3f',xv, yv, dydxv), 'Horiz','left', 'Vert','middle')

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