Question

Given a non-linear system: y=x^3 - 3x^2 - 1 a) Find the linear approximation of the system at the point (1, -3) b) Plot the system and its linear approximation on a same plot using Matlab. Make sure your plot is clear and having labeling

Answer 1

$\mbox{First, we compute the derivative of y at x_0=1 . So, we get}\\ y' = 3x^2 - 6x \, , \, y'(1) = -3$.

Therefore, the linear approximation at the point (1,-3) is

$y = -3 - 3(x -1) \ .$