Evaluate symbolic nthroot and return its symbolic expression to plot

syms x;
f(x) = ((1 + x)^(1/3));
Ln = functionLinear(f, 2);
disp(LN);

Define the function that will return the tangent line 'res' symbolically. This way I can plot both the actual function and the tangent evaluated at point 'a'. The below function is what I coded, and I am not able to get the symbolic expression back.

function[res] = functionLinear(func, a)
syms x;
g(x) = diff(func);
res = g(a)*(x-a) + func(a);
end

Answer 1

[John D'Errico]

What is wrong with it? Did you forget to use vpa? For example, with...

a = 1.3;

I get this from your code:

res =
(10^(2/3)*23^(1/3))/10 + (10^(2/3)*23^(1/3)*(x - 13/10))/69

vpa(res)
ans =
0.19130523504288585473789120739135*x + 1.0713093162401607865321907613916

It looks pretty good to me.

ezplot(f,[0,2])
hold on
ezplot(res,[0,2])
grid on

Which as far as I can see, looks like a tangent line to that function at a==1.3. Yes, it suggests that a simple Newton's method on this function will probably get in trouble. But that is not the question here.

solve(res)
ans =
-28/5

It may explain why you were asked to try to solve this problem using Newton's method, probably as homework.