7. (a) A function is differentiable at x = a if limp-o f(ath)-f exists. For this limit h to exist, the limp-of J(ath)-f(a) must equal limp-0- f(ath)-f(@). Show that if h h f (ac) = la), f is not differentiable at x = 0. (b) The TI-84 calculator calculates the derivative of a function at a point numeri- cally. It shows that for f(x) = (x|, f'(0) = 0. It uses the difference quotient flath) -f(a-h) 2h to compute the derivative. Show why the TI-84 incorrectly calcu- lates f'(0) in this case. (c) What are some plausible reasons that the TI-84 was programmed to use f(ath) -f(a-h) 2h to compute derivatives instead of f(ath)-f(a)? h