Suppose f'(x0) = 0, f" (x0) = 0, ., f(n-1) (xo) = 0 and f(") (xo) > 0, for a C" function f. Prove that f has a local minimum at xo if n is even and that zo is neither a local maximum nor a local...

0, for a C" function f. Prove that f has a local minimum at xo if n is even and that zo is neither a local maximum nor a local minimum if n is odd. "/>
Extracted text: Suppose f'(x0) = 0, f" (x0) = 0, ., f(n-1) (xo) = 0 and f(") (xo) > 0, for a C" function f. Prove that f has a local minimum at xo if n is even and that zo is neither a local maximum nor a local minimum if n is odd.