Find the linearization of f(x)=cos(x)-sin(2x) at x = 0.

Answer 1

L(x) = f(a) + f ' (a) (x-a) , where x = a

f(x) = cosx - sin 2x
f ' (x) = -sinx - 2cos 2x

L(x) = f(0) + f ' (0) (x-0)
= 1-0 + (0-2)(x-0)
= 1 - 2x