Expii

# Linear (1st Order) Taylor Approximation - Expii

The 1st Taylor approximation of $$f(x)$$ at a point $$x=a$$ is just a linear (degree 1) polynomial, namely $P(x) = f(a) + f'(a)(x-a)^1.$ This make sense, at least, if $$f$$ is differentiable at $$x=a$$: it's just another way to phrase the tangent line approximation at a point! The intuition is that $$f(a) = P(a)$$ and $$f'(a) = P'(a)$$: the "zeroth" and first derivatives match.