Question

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a function is continuous at a point, then it is differentiable at that point.

Answer 1

See Explanation

Explanation:

If a Function is differentiable at a point c, it is also continuous at that point.

but be careful, to not assume that the inverse statement is true if a fuction is Continuous it doest not mean it is necessarily differentiable, it must satisfy the two conditions.

• the function must have one and only one tangent at x=c
• the fore mentioned tangent cannot be a vertical line.

And

If function is differentiable at a point x, then function must also be continuous at x. but The converse does not hold, a continuous function need not be differentiable.

• For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.