MATLAB: How can i construct the exact Taylor Polynomial of 4th degree around x = 2

taylor polynomial

For the function

 f =@(x) exp(x./2)-2.*x.^2+x+10

how can i construct the exact Taylor Polynomial of 4th degree around x = 2?

If you have the Symbolic Math Toolbox:

Read about vpasolve.

syms x 
F = (x^2+1)/(x+1)+(2*x^2+3)/(x+2)==0 ;
r = vpasolve(F)

r = roots([a,b,c,d,e]);
r(imag(r)~=0) = [];  %remove complex
r(r <= 0) = [];  %remove non-positive
min(r)  %now it is the smallest positive real root