Trying to do a animation of tangent line and secant line for my calc class.

Question

Bruce Griffin 2022-10-25

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评论： Carlos Guerrero García 2022-11-14

My calculus class is doing mean value theroem. I want to code something to graph a function and a secant line at two given points [a,b]

I then wanted to animate tangent lines starting from a and going to b.

my issue is that I cant think this through and remember how to code for a given value.

I was thinking of something like:

x=linspace(-10,10)

y=function of x

m=diff(y)

then creating a loop. but I cant think of how to tell the loop when x value at which loop to graph the line from

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Alex Hanes 2022-10-26

编辑：Alex Hanes 2022-10-26

在 MATLAB Online 中打开

First off, I suggest that you take a look at MATLAB's On Ramp to gain some familiarity with what you can do and how you can do them in MATLAB.

If you intend to use the numerical result of y = f(x) rather than symbolic, then it would be easiest to define your function:

a = -10; 
b = +10; 
x = linspace(a,b,256); % domain of x
y1 = sin(x);           % function

Then define your derivative with the exact function (e.g., not using diff):

y2 = cos(x); % derivative of y1

To plot the secant, you can just evaluate your function at the end points:

figure(1); clf; hold on; 
plot(y1(a),y1(b),'k-','LineWidth',2); % Plot Secant Line

To plot the derivative at each x-value, you should look at the documentation forfor loops.

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Answer 1

Carlos Guerrero García 2022-11-7

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编辑：DGM 2022-11-14

在 MATLAB Online 中打开

I hope that this script is that you're looking for:

x=-1:0.01:6; s=[-2 2];
for u=-pi/2:pi/360:4*pi;
    t=3+2*sin(u);
    plot(x,2+((x-1)/2).^2,[-0.5 6],[0.5 7],[0 0],[-2 8],'k',[-2 8],[0 0],'k');
    hold on;
    plot(t+s*2/sqrt(4+(t-1)^2),2+((t-1)/2)^2+s*(t-1)/sqrt(4+(t-1)^2),'k');
    plot(t,2+((t-1)/2)^2,'.k','MarkerSize',20);
    axis equal; axis off;
    drawnow;
    hold off; 
end