how to plot a tangent line of specific point (x,y) of function y=x^2+2?

I trying to obtain the tangent equation and draw the line from specific points (x,y) of the function y=x^2+2 and show them on a figure.

Answer 1

[Image Analyst]

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);

[Hadgh]

y'=e^x

[Sam Chak]

@Hadgh, This looks like a differential equation and it is unstable because the rate of change is growing exponentially for x.

In fact, such exponential function is also infinitely differentiable. You can take the derivative of the exponential function an infinite number of times, and the result will always be another exponential function.

Wanna try it in MATLAB?

syms f(x)

f   = exp(x)

f = 

df  = diff(f)

df = 

d2f = diff(df)

d2f = 

d3f = diff(d2f)

d3f =