Math Calculus Worksheet Chap 2: Differentiation Section: Name: Mr. Lin 3 20. Example: Determined the following functions are continuous, differentiable, neither, or both at the point. (a) Continuous ____ Differentiable ____ Neither ____ (b) Continuous ____ Differentiable ____ Neither ____ (c) Continuous ____ Differentiable ____ Neither ____ (d) Continuous ____ Differentiable ____ Neither ____ (e) Continuous ____ Differentiable ____ Neither ____ (f) Continuous ____ Differentiable ____ Neither ____ (g) Continuous ____ Differentiable ____ Neither ____ (h) Continuous ____ Differentiable ____ Neither ____ 21. Example: Given the following graph, at what points does the function appear to be: (a) Continuous but not differentiable— ______________________________________________ (b) Neither continuous nor differentiable— ______________________________________________ 22. Example: Discuss the continuity and differentiability of the function f(x) = |x – 2|. 23. Example: Discuss the continuity and differentiability of the function f(x) = x 1/3 . 24. Example: Find if f(x) is continuous and/or differentiable at x = –1. () = ! + − 3 ≥ −1 − − 4 < −1 . 25. Example: Find if f(x) is continuous and/or differentiable at x = 2. () = ! − 6 + 10 ≥ 2 4 − < 2 . 26. Example: Find the value a and b that make the function f(x) differentiable. () = ! + 1 ≥ 1 − 3 < 1 .