What does it mean if a function is twice differentiable?

it means you have to derive it twice ,which means you have to derive its second order derivative ,for example derivig the distance formula gives you the speed,then deriving the speed which is the 1st derivative of distance gives you the acceleration.

Define Differentiable

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RE:

What does it mean if a function is twice differentiable?

Does it mean you can take its derivative twice, or you need to antiderive it twice to get to your original function?

What Does Differentiable Mean

Suppose a function f is defined on an interval I. Then this function is called twice differentiable (in I) if its derivative function f’ is differentiable (in I). The function f” (say: “f-double-prime”) that assigns the value f”(x) to every x∈I, is called second derivative (function) of f in I.

Analogously, f is called three times differentiable if f” is differentiable, and this third derivative of f in I is denoted by f”’.

For even higher derivatives one normally uses another notation. For every n∈ℕ, one uses f(n) to denote the n-th derivative of f in I, i.e., the derivative function of the function f(n-1) (defined inductively), given that f is n-times differentiable. In this sense we have

f(0)=f, f(1)=f’, f(2)=f”, f(3)=f”’, etc.

Some functions aren’t differentiable. So if a function is twice differentiable that means its derivative is again another differentiable function and so you can differentiate it again to obtain the 2nd derivative of the original function.

http://en.wikipedia.org/wiki/Derivative#Differenti…

the second part of the question is not answered as whether it should be of second order?? as the third order may be differentiated thrice, will it still be called a twice differentiable function?

you can differentiate it twice. for example: 2x^2+3x

first derivative:4x+3

second derivative:4

differentiate the differentiable

In other words, find the derivative of the function, then just find the derivative of the derivative.

I’m pretty sure you take its derirative twice