f(x+h) = f(x) + h f'(x) + h^2 f''(x)/2 + ...
This is what the Greeks are. Delta is the first-order term and gamma the second, so a delta-gamma approximation to an option's P&L is literally a truncated Taylor series.
Worth having memorised: e^x ≈ 1 + x, ln(1+x) ≈ x - x^2/2, (1+x)^n ≈ 1 + nx for small x. These power a lot of fast mental approximations, including why volatility drag is about sigma^2/2.