Calculus Writing Assignment: Differentiability Each question is worth 5 points. Total: 50 Points Answer each of the following questions. Make sure to show your work. 1) If possible, give an example of where a function is differentiable at a point but not continuous at that point. 2) If possible, give an example of where a function is continuous at a point but not differentiable at that point. 3) Without a graph, how can one show differentiability of a function at a point? 4) Where is the function g(x) = 3x 2 - x + 5 differentiable? 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown. 6) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown. x + 1, x < 1 7) Determine if the function f ( x ) = is differentiable at x = 1. 2 x , x 1 x + 1, x < 1 8) Determine if the function g ( x ) = is differentiable at x = 1. 2 x , x > 1 9) Where is the function h(t ) = (t + 5)1/3 differentiable? 4 x, x 0 10) Determine if the function y ( x ) = is differentiable at x = 0. 3 x, x > 0