Question

where is y=sqrt(x-1) differentiable?

Answer 1

Do you know what differentiable means?

Answer 2

yes, where the function is continuous

Answer 3

And where is function continuous?

Answer 4

x is greater than or equal to 1?

Answer 5

y = sqrt(x-1)


y = (x-1)^(1/2)


y' = (1/2)(x-1)^(-1/2)


y' = 1/(2*(x-1)^(1/2))


y' = 1/(2*sqrt(x-1))


Notice how the domain of y' is the set of numbers that are greater than 1


So y = sqrt(x-1) is differentiable when x > 1

Answer 6

so it's only greater than and not equal to 1?

Answer 7

exactly, it's not differentiable at x = 1

Answer 8

and if you graph y = sqrt(x-1), you'll see that the endpoint is at x = 1, which means there is no possible way to find the derivative here