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[answered] Calculus Writing Assignment: Differentiability Each questio

If possible, give an example of where a function is differentiable at a point but not continuous at thatpoint

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

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