Question

3. Prove that the function h(x) = √x is continuous at c = 1.
4. Prove that the function h(x) = √x is differentiable at c = 1.

Answer 1

If f is differentiable at c, then it is continuous at c. So strictly i think you need only do 4 to prove both. it will be differentiable at c if f'(c) exists. so differentiate the function and plug in the value.

Answer 2

what is your definition of continuity?
... differentiable?