5. [RECIPROCAL RULE] Suppose that f is differentiable at a and f

(a) # O.

(a) Show that for h sufficiently small, f(a + h) # O.

(b) Using Definition 4.1 directly, prove that 1/ f(x) is differentiable at x = a and

( 1)' f'

(a) 7

(a) = - J2(a)'