How do you check whether the function is differentiable or not?

A function is formally considered differentiable if its derivative exists at each point in its domain, but what does this mean? It means that a function is differentiable everywhere its derivative is defined. So, as long as you can evaluate the derivative at every point on the curve, the function is differentiable.

How do you find where a function is not differentiable?

A function is not differentiable at a if its graph has a vertical tangent line at a. The tangent line to the curve becomes steeper as x approaches a until it becomes a vertical line. Since the slope of a vertical line is undefined, the function is not differentiable in this case.

How do you tell if a function is differentiable without a graph?

If a graph has a sharp corner at a point, then the function is not differentiable at that point. If a graph has a break at a point, then the function is not differentiable at that point. If a graph has a vertical tangent line at a point, then the function is not differentiable at that point.

How do you determine the relationship between differentiability and continuity of a function?

A function is differentiable if it has a derivative. You can think of a derivative of a function as its slope. The relationship between continuous functions and differentiability is– all differentiable functions are continuous but not all continuous functions are differentiable.

How to prove differentiability at a point?

To find the differentiability we have to find the slope of the function which we can find by finding the derivative of the function [x] at point 2.5 f'(x) = d{x} / dx at x = 1.5 = 1 Therefore, the function {x} is differentiable at non-integer points.

What is continuous but not differentiable?

At zero, the function is continuous but not differentiable. If f is differentiable at a point x0, then f must also be continuous at x0. In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable.

Is a cusp differentiable?

A function which jumps is not differentiable at the jump nor is one which has a cusp, like |x| has at x = 0. Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x. There are however stranger things.

What does differentiable mean in calculus?

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.