Tangent line to a curve at a given point

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)

[Jan]

"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.

Answer 1

[Azzi Abdelmalek]

%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

[Jan]

gradient(y,t) is better than diff(y)/diff(t), because it applies a 2nd order method. At least this is true for numerical differentiation. Does this concern symbolic operations also? I cannot test this, because I do not have the symbolic toolbox.

[Christopher Creutzig]

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]

what is the use of the tang equation you used?

could you please explain it?

Answer 2

[Varun Kumar]

2*(x^(1/2)) 1,2