Suppose that f: = (u, v): R R2 is C2 and that (x0, y0) = f(t0)- a) Prove that if f(t0) 0, then

Suppose that f: = (u, v): R → R2 is C2 and that (x0, y0) = f(t0)-
a) Prove that if fʹ(t0) ≠ 0, then u'(t0) and v'(t0) cannot both be zero.
b) If fʹ(t0) ≠ 0, show that either there is a C1 function g such that g(x0) = t0 and u(g(x)) = x for x near x0, or there is a C1 function h such that h(y0) = t0 and v(h(y)) = y for y near y0.