(a) Show that the function $f(x)=x^3+x^2-2$ has a local minimum at $x=0$.
(b) Expand this function in a Taylor series around the point $x=0$, up to the fourth-order term (the term in $x^4$ ).
(c) If we keep terms only to order $x^2$, what is the range in $x$ for which our error is less than $10 \%$ ?