Why is square root function not differentiable?

If x – 1 < 0 (that is x < 1) then √(x – 1) doesn’t exist and hence x is not in the domain of the function. Hence f(x) = √(x – 1) is not differentiable if x < 1. as h approaches zero. In this case when h < 0 the square root doesn’t exist and hence the limit can’t exist.

Why is cube root x not differentiable?

Cube root It looks like the slope gets pretty big near the red dot. In fact, the cube root function has a vertical tangent at x = 0, which means that the limit in the derivative is undefined at this point. Hence this function is not differentiable at x = 0.

What makes a derivative not differentiable?

Graphical Meaning of non differentiability. We can say that f is not differentiable for any value of x where a tangent cannot ‘exist’ or the tangent exists but is vertical (vertical line has undefined slope, hence undefined derivative).

Is MOD x 3 differentiable?

x^3 | is differentiable at x = 0 .

Is X cubed differentiable?

Originally Answered: Is |x|^3 differentiable at x=0? Yes it is differentiable at x=0. To check that first you have to define the function for x>0 and x<0.

Which of the following function is not differentiable?

Discontinuous function is always non differentiable.

Why is the derivative of a function not differentiable at 0?

And the point you are missing is just that everyone is saying what you are- the limit defining the derivative at 0 does not exist so is not differentiable at x= 0. Alright so essentially you’re saying im right. Just the fact that a line is a line and not based on a function itself.

Can a derivative ever be vertical?

While a derivative can get very very close to being vertical This is badly stated. A derivative is a function, not a line, so “being vertical” makes no sense. , I was taught once it’s vertical it’s no longer a function and is undefined at that point.

What is the derivative of the tangent line at x = 0?

The tangent line is vertical at x = 0. So the slope of the tangent line is undefined. Therefore the function that represents the slope of the tangent line is undefined at x = 0. Which is another way of saying the derivative is undefined at x = 0.