these true or false

True or False: [7 Marks] 9. A piecewise function can be continuous everywhere but not differentiable everywhere. 10. If a function f(x) is continuous in an open interval, then f(x) has both a maximum value and a minimum value. 11. If the limit exists at x = a, then the function is continuous at x = a 12. If the left-hand limit and the right-hand limit of a function exist at a point x = a, then the limit at x = a exists. 13. Instantaneous rate of change can be estimated by finding the difference quotient over a very small interval. 14. An infinite discontinuity means a function is merely a set of scattered points. 15. A piecewise function always has jump discontinuity