Plot the line Tangent at a given point

I'm new to Matlab and am trying to plot the following:

Graph the function y = 3x^2 for x = 0 to x = 5 in steps of 0.1 as a solid blue line.

On the same plot, graph the equation of the line tangent to y = 3x^2 at x = 2 as a dashed red line.

I got the first part done. Just can't figure out how to plot the line tangent.

[Voss]

What did you figure out so far about the tangent line? Do you know its slope? Did you figure out an equation for it?

Answer 1

[Sam Chak]

Hi @ILoveMath

As a self-proclaimed math lover, I presume that you already know mathematically how to find the tangent line by hand.

If you are asking how to find the slope the MATLAB way, here is one of several approaches:

h = 0.001;                              % step size
x = 0:h:5;
y = 3*x.^2;                             % the function, f(x)
plot(x, y, 'linewidth', 1.5)
hold on                                 % retain current figure
p = 2;                                  % x = 2
plot(p, 3*p^2, 'o', 'linewidth', 1.5)	% display the point at y(2)

w = gradient(y)/h;                      % compute the slope of the function
m = w(p/h + 1);                         % slope at x = 2
c = y(p/h + 1) - m*x(p/h + 1);          % y-intercept
z = m*x + c;                            % line equation at x = 2
plot(x, z, 'linewidth', 1.5)
hold off

grid on
xlabel('x')
ylabel('y')
title('y = f(x) and the tangent line at x = 2')
legend('function f(x)', 'the point at y(2)', 'tangent line at x = 2', 'location', 'northwest')

[Star Strider]

It is not considered appropriate to provide a complete solution to homework problems.