# N this discussion, you will create a function that is both continuous and differentiable at a particular point. Without first

n this discussion, you will create a function that is both continuous and differentiable at a particular point. Without first creating a function, assign values to a function and its derivative for a particular value of x. For example, state that and . Create a function f such that the function satisfies the given conditions and is both continuous and differentiable at that value of x. Write the function and describe how you found it. 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 of x. As a challenge for your classmates, state values of a new function and its derivative at a particular value of x and ask them to create a function g such that the function is both continuous and differentiable at that value of x. Be sure to reply to at least two other classmates’ posts. Each reply will involve creating a function that satisfies the conditions given to you and is both continuous and differentiable at the given value of x.

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