Tangent line to a curve at a given point

Question

x y 2013-10-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/89306-tangent-line-to-a-curve-at-a-given-point

回答： Varun Kumar 2019-11-2

采纳的回答： Azzi Abdelmalek

在 MATLAB Online 中打开

Hy, I want to plot tangent line for function given by one point.

I tried to solve this problem but didnt work well Someone can me help me,pls

syms x
func = -2*x^2+4;
x0 = 1;
% f(x)'= -4*x
m=diff(func)
% m == f(x0)'= -4*x0
fdx = inline(m, 'x');
fdx(x0)
% x == (x - x0)
xX =(x - x0) 
% c == f(x0)
fx = inline('-2*x^2+4', 'x');
c = fx(x0)
ezplot(x)
hold on
% y = m*x + c
y=m*xX+c;
ezplot(y)

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Jan 2013-10-6

"Didn't work well" is a DON'T in a forum. Do not let us guess the problems, but explain them to save the time of the readers. The less the readers have to guess, the more likely is a matching answer.

请先登录，再进行评论。

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Answer 1

Azzi Abdelmalek 2013-10-6

5
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/89306-tangent-line-to-a-curve-at-a-given-point#answer_98752

编辑：Azzi Abdelmalek 2013-10-6

在 MATLAB Online 中打开

%Example
t=0:0.01:10
y=sin(t)
plot(t,y)
%-------------------------
dy=diff(y)./diff(t)
k=220; % point number 220
tang=(t-t(k))*dy(k)+y(k)
hold on
plot(t,tang)
scatter(t(k),y(k))
hold off

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Christopher Creutzig 2013-11-8

I don't see symbolic in Azzi's answer, but as to your question: if y is symbolic, then diff(y) (or diff(y,t)) is exact and there is no room for some “more precise” way of getting a symbolic derivative. (Which is not to say that for some applications, getting higher order approximations like taylor(y,t) might not be better. But again, those are exact.)

Numerically, integration is easy and differentiating is hard. (Hard as in: Hard to get any kind of reliable answers for a wide range of functions.) Symbolically, it's the other way round: Differentiating is dead easy, integrating is still more of an art than a science.

noora alahmed 2019-10-7