I don't understand a part of the solution to c) of this problem, namely linearization at a stationary point using Taylor series and partial derivatives.
I am used to linearization of \$ f(x,u) \$ (two variables) using Taylor series but not \$ f(x_1,x_2,u) \$ (three variables) at a stationary point.
Are we supposed to linearize using Taylor series for three variables or just find the partial derivative of \$f_1\$ and \$ f_2 \$? We get a term \$ f(x^0_1,x^0_2,u^0) \$ (which looks like \$ f(a,b) \$ from Taylor series formula for two variables above) present in the solution which is set to zero that is not present if we were to just find the partial derivative of \$f \$ with respect to all terms and just sum them up?
Sorry if the question is a bit messy since I have trouble connecting the mathematical theory with the control theory.