In this discussion, you will create a function that is both continuous and differentiable at a particular point.

1. Without first creating a function, assign values to a function and its derivative for a particular value ofx. For example, state thatand.
2. Create a functionfsuch that the function satisfies the given conditions and is both continuous and differentiable at that value ofx. Write the function and describe how you found it.
3. Use the limit definitions of continuity at a point and differentiability at a point to prove that your function is both continuous and differentiable at that value ofx.
4. As a challenge for your classmates, state values of a new function and its derivative at a particular value ofxand ask them to create a functiongsuch that the function is both continuous and differentiable at that value ofx.