Derivative of an endpoint?

Question

can u find the derivative of an endpoint or does it not exist...

Answer 1

Consider f(x) = sqrt(x).

The domain of f(x) is [0, infinity).

Range is also [0, infinity)

What would be the derivative of f(x) at x = 0 ?

In lots of functions with a domain that is naturally limited, like f(x), the derivative does not exist at an endpoint.

But, if you choose to limit the domain of a function (and in some word problems you have to), the tangent line to the function at the endpoint will not be vertical and the derivative will exist.

For example, if g(x) = 3x with a domain of [0, infinity), (0, 0) is an endpoint of the straight line g(x) for which the derivative is 3 throughout the domain.