Try this:
x = linspace(-2, 2, 500);
y = x .^ 2 + 2;
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
fontSize = 20;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
ylim([0, 7]);
% Pick a point at -1 (or wherever) and plot the tangent
xTangent = -1;
% Equation of the tangent is y = slope*x + offset
% From the equation y=x^2 we know the slope is 2*x.
% Find the slope at x = xTangent.
slope = 2 * xTangent;
% We want to plot the tangent line where it just touches the curve,
% so we need to know the y value at xTangent.
yTangent = xTangent .^ 2 + 2; % Y value of curve at x = xTangent.
hold on;
plot(xTangent, yTangent, 'r*', 'LineWidth', 2, 'MarkerSize', 10);
% Use point slope formula of a line to get equation for y
% y-y0 = slope*(x-x0).
% y = slope * (x - xTangent) + yOffset
yTangentLine = slope * (x - xTangent) + yTangent;
plot(x, yTangentLine, 'b-', 'LineWidth', 2);
