What does it mean if a function is twice differentiable?

Question

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

Lilyan Mitchell · Accepted Answer

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.

Lilyan Mitchell · Answer

Define Differentiable

Lilyan Mitchell · Answer

This Site Might Help You.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?

Lilyan Mitchell · Answer

What Does Differentiable Mean

Lilyan Mitchell · Answer

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

Lilyan Mitchell · Answer

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…

Lilyan Mitchell · Answer

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?

Lilyan Mitchell · Answer

you can differentiate it twice. for example: 2x^2+3xfirst derivative:4x+3second derivative:4

Lilyan Mitchell · Answer

differentiate the differentiableIn other words, find the derivative of the function, then just find the derivative of the derivative.

Lilyan Mitchell · Answer

I’m pretty sure you take its derirative twice

Ms. Lavinia Lowe IV

What does it mean if a function is twice differentiable?

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