Critical points satisfy ( \nabla f = 0 ). The second derivative test uses the Hessian determinant ( H = f_xx f_yy - (f_xy)^2 ):
Given a function ( f ), its indefinite integral is a family of functions ( F(x) + C ) such that ( F'(x) = f(x) ). The fundamental techniques include:
Pointwise convergence is weak. ( ( \sup_x |f_n(x) - f(x)| \to 0 ) ) preserves continuity, integrability, and differentiability of the limit function. The Weierstrass M-test is a key tool.